Trying to get my head around off-grid and batteries!

jars121
jars121 Registered Users Posts: 7 ✭
in Off Grid Solar & Battery Systems #1
Hi all,

I've hypothetically looking at designing an 8kW off-grid PV installation, with a battery back-up system. This project is in partnership with another person (who will benefit from this system), and as of now I'm not entirely sure of their daily load profile. Is it safe to assume 3 days of autonomy when it comes to sizing the battery system, or is there no particular standard?

Assuming I did want 3 days of continuous, 8kW autonomy from the batteries, I'd be looking at 8kW x 24 hrs/day x 3 days = 576kWh (which would cost around $80,000 with a 24VDC configuration)? Perhaps my understanding of days of autonomy is incorrect, but this seems really expensive!

Any clarification would be great. I will endeavour to clarify with the other partner what usage profiles they will be using the system with.

Thanks!
· Share on Twitter
«1

Comments

  • Cariboocoot
    Cariboocoot Banned Posts: 17,615 ✭✭✭
    #2
    Re: Trying to get my head around off-grid and batteries!

    Welcome to the forum.

    First of all (just to nit-pick), off-grid doesn't have battery back-up; it runs from batteries.

    Second, the 3 days autonomy choice is a sure-fire way to make an expensive system.

    Third, "8kW" is not the whole story; the power quantity is expressed in Watt hours. So 8 kW hours would be the target, and it's a fairly large one for off-grid.

    On 24 Volts it would be roughly (8000 Watt hours / 24) 334 Amp hours, meaning a minimum battery bank of 668 Amp hours just for one day. For two days double that and for three days triple it. See what I mean about expensive?

    Anyway, this is 48 Volt system territory; double the Voltage, halve the current. At that level the 668 Amp hours would do for 25% DOD per day allowing up to two days use if needed. Day #3; start the gen.

    That is leaving out inverter consumption and conversion losses, btw.

    First rule of off-grid: reduce the power needs as much as possible. It's expensive to produce power this way, so the less you need the more you save.
    · Share on Twitter
  • niel
    niel Solar Expert Posts: 10,300 ✭✭✭✭
    #3
    Re: Trying to get my head around off-grid and batteries!

    welcome,
    actually your figures are off by 2x. you would need to double the ah capacity to keep from going below 50% soc. get what you can for your autonomy, but 1 day would be minimum with 50% of the charge in reserve for battery life reasons and as a possible emergency power in dire times that would damage the battery lifespan. batteries as you point out are expensive and pv prices are dropping. go with extra pv to help get the bank topped off faster, but keep the charge rate limited so as to not feed them more than the manufacturers of the batteries recommend. most agm batteries can take 20% charge rates with some much higher. fla batteries may also be able to go more than the 13% minimum we recommend, but this does have its limits and would entail higher maintenance.

    of course a generator or another source of power is a good idea too because of the high cost of storing power in batteries.
    · Share on Twitter
  • jars121
    jars121 Registered Users Posts: 7 ✭
    #4
    Re: Trying to get my head around off-grid and batteries!

    Thanks!

    I'm not sure about the power definition you've given though. Watt hours is a measure of energy, whereas Watts is a measure of power. The 8kW system I'm desinging will therefore supply 8kW of power, which is 8kWh of energy for every hour it runs at 100% capacity.

    As such, assuming 6 peak sun hours a day, that's around 48kWh of generated energy per day, which is the equivalent of 1000Ah/day (at 48VDC)?

    I'm just rambling here, I'm not sure whether this is correct or not. From what I've gathered though, a 3 day autonomy is unnecessary. Thanks again!
    · Share on Twitter
  • Cariboocoot
    Cariboocoot Banned Posts: 17,615 ✭✭✭
    #5
    Re: Trying to get my head around off-grid and batteries!
    jars121 wrote: »
    Thanks!

    I'm not sure about the power definition you've given though. Watt hours is a measure of energy, whereas Watts is a measure of power. The 8kW system I'm desinging will therefore supply 8kW of power, which is 8kWh of energy for every hour it runs at 100% capacity.

    As such, assuming 6 peak sun hours a day, that's around 48kWh of generated energy per day, which is the equivalent of 1000Ah/day (at 48VDC)?

    I'm just rambling here, I'm not sure whether this is correct or not. From what I've gathered though, a 3 day autonomy is unnecessary. Thanks again!

    8kW per hour? (We need a "smiley" for "mortified".)

    Okay, that's not right. Off grid systems are designed around the daily usage in Watt hours. This is supplied by the batteries. The batteries are recharged by the PV array.

    You are looking at it from a grid-tie point of view, where an 8kW array would feed an average of 6 kW of power to the "unlimited battery" that is the power grid over 6 hours of equivalent good sun (unlikely) resulting in a daily harvest of 36kW hours per day.

    Off grid just does not work like that. Once the batteries are fully recharged, any further power potential from the array is not utilized unless you create some place for it to go in the form of "opportunity loads".

    If you want to get 48kW hours of power off-grid you need over 2,000 Amp hours of 48 Volt battery per day, plus about 18kW of panel to recharge it.

    An 8kW array would typically produce 20kW hours AC off grid on a good day.
    · Share on Twitter
  • jars121
    jars121 Registered Users Posts: 7 ✭
    #6
    Re: Trying to get my head around off-grid and batteries!

    I'm getting really confused. 8kW per hour?!? I said 8kWh (a unit of energy) when the panels are outputting 8kW over an hour's duration (power x time = energy).

    I'm definitely looking at it from a grid-tie point of view, as that's where my experience lies :p

    I've avoided batteries as long as possible, but I think they will inevitably be part of my future! There is the potential for a generator to be thrown into the mix with this setup as well, so I really don't have enough detail at the moment to put together a strategy, I just wanted to have some things clarified, which you have done :) I definitely have some research to do! Thanks!
    · Share on Twitter
  • ChrisOlson
    ChrisOlson Banned Posts: 1,807 ✭✭
    #7
    Re: Trying to get my head around off-grid and batteries!

    Most of the basics have already been covered. I can only add that there is so many things to look at and pencil out to make your investment in batteries the smallest possible. The batteries will be the most expensive part of an off-grid power system - usually costing more over the long term for JUST the batteries and their eventual replacement than it costs to buy the equivalent energy from the grid that you will store and use in them over their useful life.

    In case you didn't fully absorb that, read it again. Living off-grid is expensive - big time. All it takes is Cubic Money to set up a decent sized off-grid power system. And once you have it set up, prepare to shell out more Cubic Money every 7 years or so when the batteries wear out.

    It is wise to know what your consumption is going to be, what the peak loads are, and whether or not you can use things like Generator Support for peak loads with a suitable inverter to reduce your investment and cost in batteries long term.
    --
    Chris
    · Share on Twitter
  • Cariboocoot
    Cariboocoot Banned Posts: 17,615 ✭✭✭
    #8
    Re: Trying to get my head around off-grid and batteries!

    If you have an 8kW array running for one hour it produces 8kW hours (disregard losses). It is presumed it will continue to do so for as many hours as it is subjected to full sun: 8kW per hour.

    The difference is the GT is looked at from an array production point of view where as OG has to be looked at from a Watt hours consumption point of view. Otherwise it tends not to work. Often in a very expensive and frustrating way. :p
    · Share on Twitter
  • jars121
    jars121 Registered Users Posts: 7 ✭
    #9
    Re: Trying to get my head around off-grid and batteries!
    Cariboocoot wrote: »
    If you have an 8kW array running for one hour it produces 8kW hours (disregard losses). It is presumed it will continue to do so for as many hours as it is subjected to full sun: 8kW per hour.

    *8kWh per hour (peak).

    I agree with everything else you said haha.
    · Share on Twitter
  • ChrisOlson
    ChrisOlson Banned Posts: 1,807 ✭✭
    #10
    Re: Trying to get my head around off-grid and batteries!
    jars121 wrote: »
    *8kWh per hour (peak).

    8 kWh is 8 kW per hour. It can also be expressed as 8 kW.h

    While we all understand that you're trying to say that you're producing 8 kWh of energy every hour, using the term "8 kWh per hour" is incorrect. 8 kW per hour is the correct terminology.
    --
    Chris
    · Share on Twitter
  • vtmaps
    vtmaps Solar Expert Posts: 3,741 ✭✭✭✭
    #11
    Re: Trying to get my head around off-grid and batteries!
    ChrisOlson wrote: »
    8 kW per hour is the correct terminology.

    Why the 'per hour'? Just say 8 kw. A watt is a rate of energy use. Watts per hour is a rate of a rate. If I am producing 5 kw at noon and 13 kw at 1 pm and 21 kw at 2 pm, then my power is increasing at 8 kw per hour. --vtMaps
    4 X 235watt Samsung, Midnite ePanel, Outback VFX3524 FM60 & mate, 4 Interstate L16, trimetric, Honda eu2000i
    · Share on Twitter
  • jars121
    jars121 Registered Users Posts: 7 ✭
    #12
    Re: Trying to get my head around off-grid and batteries!
    vtmaps wrote: »
    Why the 'per hour'? Just say 8 kw. A watt is a rate of energy use. Watts per hour is a rate of a rate. If I am producing 5 kw at noon and 13 kw at 1 pm and 21 kw at 2 pm, then my power is increasing at 8 kw per hour. --vtMaps

    This is the issue I'm having with the kW per hour terminology. As far as I'm concerned, kWh per hour is a perfectly legitimately way of expressing it; it's stating a unit of energy per time.
    · Share on Twitter
  • BB.
    BB. Super Moderators, Administrators Posts: 33,649 admin
    #13
    Re: Trying to get my head around off-grid and batteries!
    Cariboocoot wrote: »
    If you have an 8kW array running for one hour it produces 8kW hours (disregard losses). It is presumed it will continue to do so for as many hours as it is subjected to full sun: 8kW per hour.

    The difference is the GT is looked at from an array production point of view where as OG has to be looked at from a Watt hours consumption point of view. Otherwise it tends not to work. Often in a very expensive and frustrating way. :p

    Just to be nit-picking... it is actually (Marc is trying to explain a different way to make it clear--but the math is):
    • 8kWH per hour which equals 8kW solar array (or load, or whatever)... (8 kWatt per hour) * hours = 8kW (hours cancel out)

    You are correct... Watts is a "rate" (like miles per hour) and Watt*Hours is an amount (like miles driven). (and k=1,000 times).

    So, you can have an 8 kW load running 24 hours per day:
    • 8 kW * 24 hours = 192 kWH per day = 192,000 WH per day

    Or you can have an 8 kWH per day load = 8,000 WH per day

    So, everyone is just trying to understand the loads. In general, a "nice" off grid system for a cabin or small/very energy efficient home is around 3.3 kWH per day or 100 kWH per month.

    The average grid connected home in North America is probably close to 1,000 kWH per month loads. Which, many times, can be cut down by close to 1/2 with lots of conservation, insulation, energy star appliances, etc...

    While it is certainly possible to make a 192 kWH per day worth of solar power... It is going to be expensive and, probably, in the realm of a fully engineered design using large equipment that we, as a forum, do not usually use (although, there are quite a few systems that are simply a large battery bank and a whole bunch of "high end" home/small business type solar RE equipment (i.e., bunch of ~6kW inverters and ~80 amp charge controllers on a very large 48 volt battery bank).

    In the end, for north America, as a first approximation most places in reasonably sunny areas in the US get around 4 hours of sun per day for ~9 months of the year. And the overall system efficiency is around 0.52 (from solar panel marketing numbers to the AC inverter's outlet). So, a 192,000 WH per day load would need around:
    • 192,000 WH * 1/0.52 off grid system efficiency * 1/4 hours of sun "break even" point = 92,308 solar array (break even ~4 hours)

    The above number is probably within 10% for a back of the envelope calculation.

    And if you wanted 2 days of storage with a maximum of 50% discharge:
    • 192,000 WH per day * 1/0.85 inverter efficiency * 2 days of storage * 1/0.50 max discharge * 1/48 volt battery bank = 18,824 AH @ 48 volt battery bank nominal

    Now, the above assumes charging during the day and discharging at night... If your loads are full time during the day, or mostly during the day, you could talk about a smaller battery bank (unless you still need the storage for "dark days").

    We also talk about 5% to 13% average rate of charge for a battery bank "as seen by the battery bank"... So if you have constant loads during the day, they have to be added to the solar array output to ensure the battery gets sufficient charging current (especially if you size the array towards the 5% rate of charge at the low end). A nice 10% rate of charge array to battery bank ratio would look like:
    • 18,824 AH * 59 volts charging * 1/0.77 panel+controller deratings * 0.10 rate of charge = 144,236 Watt array based on 10% battery bank rate of charge

    "Industrial/Forklift" batteries tend to need higher rates of charge (check the manuals)--So, you can see pushing a battery bank larger will also have an effect on the solar array minimum sizing too.

    -Bill
    Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
    · Share on Twitter
  • Cariboocoot
    Cariboocoot Banned Posts: 17,615 ✭✭✭
    #14
    Re: Trying to get my head around off-grid and batteries!

    vtMaps is correct: Watt per hour doesn't exist. Watts for an hour is another matter.

    It all depends on whether you are talking about maximum or average output from panels or inverter (as with a GT system) sustain over time ('X' Watts for 'Y' hours) or quantitative amount of power ('X' Watt hours) as would be used for sizing an off-grid systems capacity.

    Got to be talking about the same thing in order to get the terms right. ;)

    Don't worry; we're working on making it even more complicated! :p
    · Share on Twitter
  • Photowhit
    Photowhit Solar Expert Posts: 6,006 ✭✭✭✭✭
    #15
    Re: Trying to get my head around off-grid and batteries!

    So, you want to do an off grid system...

    You don't have a handle on what the other person uses, do you have an idea of how much energy you use?

    Where are you doing this, the solar isolation will give you an idea of how much average exposure you will receive.

    What time of year is your greatest demand for energy, if this is winter with the higher demand for lighting and greater time spent indoors, around TV and the like this create a higher demand on your battery, if it's during the summer you will have a less need for a large battery as you have more sunlight with your demand.

    Having a generator and willing to use it will also reduce your need for a larger battery bank, of course.

    Trying to figure out the balance isn't easy when you have all the variables, not knowing what half of the users needs are will make things impossible.
    Home system 4000 watt (Evergreen) array standing, with 2 Midnite Classic Lites,  Midnite E-panel, Magnum MS4024, Prosine 1800(now backup) and Exeltech 1100(former backup...lol), 660 ah 24v Forklift battery(now 10 years old). Off grid for 20 years (if I include 8 months on a bicycle).
    - Assorted other systems, pieces and to many panels in the closet to not do more projects.
    · Share on Twitter
  • jars121
    jars121 Registered Users Posts: 7 ✭
    #16
    Re: Trying to get my head around off-grid and batteries!
    Photowhit wrote: »
    So, you want to do an off grid system...

    You don't have a handle on what the other person uses, do you have an idea of how much energy you use?

    Where are you doing this, the solar isolation will give you an idea of how much average exposure you will recieve.

    What time of year is your greatest demand for energy, if this is winter with the higher demand for lighting and greater time spent indoors, around TV and the like this create a higher demand on your battery, if it's during the summer you will have a less need for a large battery as you have more sunlight with your demand.

    Having a generator and willing to use it will also reduce your need for a larger battery bank, of course.

    Trying to figure out the balance isn't easy when you have all the variables, not knowing what half of the users needs are will make things impossible.

    Thanks for that. I appreciate that it's hard to offer advice without all the information. My associate has told me that the details of the full installation are still hush-hush (I don't know them either), so this was more for my benefit, being a complete newb with batteries. I've looked into fuel cells as well, but given the size of this project (from what I can gather), I'm not sure how practical that will be.
    · Share on Twitter
  • Cariboocoot
    Cariboocoot Banned Posts: 17,615 ✭✭✭
    #17
    Re: Trying to get my head around off-grid and batteries!

    He won't tell you the details?
    Run. Run fast, run far.
    · Share on Twitter
  • solar_dave
    solar_dave Solar Expert Posts: 2,397 ✭✭✭✭
    #18
    Re: Trying to get my head around off-grid and batteries!
    Cariboocoot wrote: »
    He won't tell you the details?
    Run. Run fast, run far.

    In the opposite direction!
    · Share on Twitter
  • mike95490
    mike95490 Solar Expert Posts: 9,583 ✭✭✭✭✭
    #19
    Re: Trying to get my head around off-grid and batteries!
    There is the potential for a generator to be thrown into the mix with this setup as well

    If you have batteries, you must either buy a generator for backup charging, or plan to replace batteries very often. In the dark.
    Powerfab top of pole PV mount | Listeroid 6/1 w/st5 gen head | XW6048 inverter/chgr | Iota 48V/15A charger | Morningstar 60A MPPT | 48V, 800A NiFe Battery (in series)| 15, Evergreen 205w "12V" PV array on pole | Midnight ePanel | Grundfos 10 SO5-9 with 3 wire Franklin Electric motor (1/2hp 240V 1ph ) on a timer for 3 hr noontime run - Runs off PV ||
    || Midnight Classic 200 | 10, Evergreen 200w in a 160VOC array ||
    || VEC1093 12V Charger | Maha C401 aa/aaa Charger | SureSine | Sunsaver MPPT 15A

    solar: http://tinyurl.com/LMR-Solar
    gen: http://tinyurl.com/LMR-Lister ,

    · Share on Twitter
  • inetdog
    inetdog Solar Expert Posts: 3,123 ✭✭✭✭
    #20
    Re: Trying to get my head around off-grid and batteries!
    Cariboocoot wrote: »
    If you have an 8kW array running for one hour it produces 8kW hours (disregard losses). It is presumed it will continue to do so for as many hours as it is subjected to full sun: 8kW per hour.

    I can see producing 8kWh per hour and producing 8kW over a one hour period, but I also have an objection to writing 8kW per hour. The closest I am willing to come is "8kW average".

    kWh / h = kW.

    The problem that I see, particularly where loads are concerned, is that there is no convenient way (using just the units abbreviation) to distinguish between talking about a load that draws 1kW whenever it is turned on (instantaneous Power) and that same load using 1kW when turned on, but only on for a 50% duty cycle, giving .5kWh/hour, or reduced .5kW (Power averaged over one hour). Just like miles per hour and *average* miles per hour over a one hour period, the units are the same. But miles per hour per hour does not serve the purpose!
    SMA SB 3000, old BP panels.
    · Share on Twitter
  • BB.
    BB. Super Moderators, Administrators Posts: 33,649 admin
    #21
    Re: Trying to get my head around off-grid and batteries!

    My youngest just "loves" the two ships leave at midnight, 700 miles apart, sailing towards each other. Ship 1 is traveling 30 MPH faster than ship 2. They crash at 10am. How fast are the ships going?

    It is enough to turn you off of math (I know it did for me until I got into college).

    -Bill
    Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
    · Share on Twitter
  • Cariboocoot
    Cariboocoot Banned Posts: 17,615 ✭✭✭
    #22
    Re: Trying to get my head around off-grid and batteries!

    When Robert Benchley wrote about it they were trains, and his answer was that if he was on one of them you could bet it would be at least ten minutes late. :p
    · Share on Twitter
  • inetdog
    inetdog Solar Expert Posts: 3,123 ✭✭✭✭
    #23
    Re: Trying to get my head around off-grid and batteries!
    BB. wrote: »
    My youngest just "loves" the two ships leave at midnight, 700 miles apart, sailing towards each other. Ship 1 is traveling 30 MPH faster than ship 2. They crash at 10am. How fast are the ships going?

    It is enough to turn you off of math (I know it did for me until I got into college).

    -Bill

    I also like the question of how far apart the two ships are when they crash.
    And that is one very fast ship!
    SMA SB 3000, old BP panels.
    · Share on Twitter
  • ChrisOlson
    ChrisOlson Banned Posts: 1,807 ✭✭
    #24
    Re: Trying to get my head around off-grid and batteries!
    inetdog wrote: »
    I can see producing 8kWh per hour and producing 8kW over a one hour period, but I also have an objection to writing 8kW per hour. The closest I am willing to come is "8kW average".

    Perhaps it's time to refer to the wiki:
    http://en.wikipedia.org/wiki/Kilowatt_hour#Confusion_of_kilowatt_hours_and_kilowatts
    jars121 wrote: »
    My associate has told me that the details of the full installation are still hush-hush (I don't know them either)

    Wow. I think I'd be finding a new associate. Like immediately. Top Secret Off-Grid Installations are best left to clandestine government operations. They typically screw everything up anyway.
    --
    Chris
    · Share on Twitter
  • inetdog
    inetdog Solar Expert Posts: 3,123 ✭✭✭✭
    #25
    Re: Trying to get my head around off-grid and batteries!
    ChrisOlson wrote: »
    Perhaps it's time to refer to the wiki:
    http://en.wikipedia.org/wiki/Kilowatt_hour#Confusion_of_kilowatt_hours_and_kilowatts

    OK, how do I produce a centered dot with the editing tools provided by the forum?

    how about this: kW.h
    That was a bold superscript period. (or full-stop for the Brits.)
    Or maybe this" kW∙h
    That was the "bullet operator" from the OS X character picker.
    Or kW•h, which uses the "bullet".
    Preferences anyone?
    SMA SB 3000, old BP panels.
    · Share on Twitter
  • ChrisOlson
    ChrisOlson Banned Posts: 1,807 ✭✭
    #26
    Re: Trying to get my head around off-grid and batteries!

    Just do it the way us brain-dead engineers have always done it - kW.h

    We've always figured that if they don't know what it means, ta' heck with 'em 8)
    --
    Chris
    · Share on Twitter
  • BB.
    BB. Super Moderators, Administrators Posts: 33,649 admin
    #27
    Re: Trying to get my head around off-grid and batteries!

    kWH -- two variables next to each other is assumed to be a multiplication---Works for me (AB = AxB).

    -Bill
    Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
    · Share on Twitter
  • ChrisOlson
    ChrisOlson Banned Posts: 1,807 ✭✭
    #28
    Re: Trying to get my head around off-grid and batteries!
    BB. wrote: »
    kWH -- two variables next to each other is assumed to be a multiplication---Works for me (AB = AxB).

    That's usually the easiest, and what most people use. But for the Dot People like engineers we've never gotten too excited about trying to figure out how to elevate that dot up to the middle, because the tools we use always put it on the bottom. So we use things like ft.lbf, hp.h, or on the metric side N.m and kW.h

    For the "normal" people it would be just lbf, hp, Nm and kWh :D

    --
    Chris
    · Share on Twitter
  • Photowhit
    Photowhit Solar Expert Posts: 6,006 ✭✭✭✭✭
    #29
    Re: Trying to get my head around off-grid and batteries!
    mike95490 wrote: »
    If you have batteries, you must either buy a generator for backup charging, or plan to replace batteries very often. In the dark.

    Or just have a well planned system, No generator for 11 years, 3 battery replacements, (one due to user error, leaving a load while gone for 3 months with panels mostly down.) Golf cart batteries until forklift battery 2 years ago.
    Home system 4000 watt (Evergreen) array standing, with 2 Midnite Classic Lites,  Midnite E-panel, Magnum MS4024, Prosine 1800(now backup) and Exeltech 1100(former backup...lol), 660 ah 24v Forklift battery(now 10 years old). Off grid for 20 years (if I include 8 months on a bicycle).
    - Assorted other systems, pieces and to many panels in the closet to not do more projects.
    · Share on Twitter
  • Photowhit
    Photowhit Solar Expert Posts: 6,006 ✭✭✭✭✭
    #30
    Re: Trying to get my head around off-grid and batteries!
    BB. wrote: »
    My youngest just "loves" the two ships leave at midnight, 700 miles apart, sailing towards each other. Ship 1 is traveling 30 MPH faster than ship 2. They crash at 10am. How fast are the ships going?

    Now there's a real problem, but Bill, you left out some variables, we know when they crashed, and I'll assume you want to know when the question was asked, ...the but how deep is the water, the water density, and residual buoyancy with the assumtion there will be no additional reduction, if we throw out surface tension, I might be able to figure it out...

    ...now do you want to know for each ship or will they be a single mass?
    Home system 4000 watt (Evergreen) array standing, with 2 Midnite Classic Lites,  Midnite E-panel, Magnum MS4024, Prosine 1800(now backup) and Exeltech 1100(former backup...lol), 660 ah 24v Forklift battery(now 10 years old). Off grid for 20 years (if I include 8 months on a bicycle).
    - Assorted other systems, pieces and to many panels in the closet to not do more projects.
    · Share on Twitter
  • niel
    niel Solar Expert Posts: 10,300 ✭✭✭✭
    #31
    Re: Trying to get my head around off-grid and batteries!

    i could be a smarta** and say too fast.

    all kidding aside i looked at it from the perspective if 1 ship did not move firstly and the other would travel 700 miles in 10hrs. this is 70mph as the total speed for that time and distance between the ships. that means that with the other ship moving that it is a speed that when adding 30 to it gives you the other speed that both speeds total to 70mph. 20mph + 50mph = 70mph. problem solved.
    · Share on Twitter

Categories