Source: Not sure. Don't think it is OG. Just a problem my friend and I are trying to do. I've changed the wording around a bit to avoid any copyright issues.
Just want to see if answer I am getting is correct.
Pool holds 450 cubic meters of H2O. Hose fills pool at rate of 6 cubic meters/minute. Pool has hole which lets out H2O at .5 cubic meters/minute. How long will it take to fill to capacity?
I did this problem 2 ways:
1) Hose can complete 1/75 of the job in 1 minute; Hole completes 1/900 (drains) in 1 minute. Two working together= 1/75-1/900=1/A
A=1/81 of the job in a minute or the entire job takes 81 9/11 minutes.
2) If Hose fills at 6 cubic meters and hole drains at .5 cubmic meters per minute then working together 5.5 cubic meters/minute of water is added to the pool. Therefore 450/5.5= 81 and 9/11 minutes.
Can a MGMAT Guru corroborate my thinking and point out if this is the way you would approach?
Thanks.
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Working together
Those are pretty un-OG-like numbers, so I believe you about the source :-)
Anyway, both approaches are correct, but the second approach (adding the rates) is better than the first (working together formula), in my opinion. Several reasons:
1) There are fewer steps in the calculation.
2) The calculation steps themselves are easier (450/5.5 = 4500/55 = 900/11 is much better than 1/75 - 1/900 = 12/900 - 1/900 = 11/900 = 1/A, therefore A = 900/11) In fact, your explanation for the first approach threw me because I think there is an error/typo in it: 1/A does not equal 1/81 exactly--looks like you might have been approximating because the calculation was such a pain!
3) They give you the rates outright--you can immediately combine them, no preliminary calculations required.
You might note that the "working together formula" and "adding the rates to get the combined rate" are the same thing--the formula is based on adding the rates. So what's the distinction? The "working together formula" is more useful for problems in which you don't know one of the individual rates, but are given the combined rate. The "adding the rates" shortcut is most useful on problems (such as this one) in which you know the individual rates and are asked to calculate the total time, or less likely, simply the combined rate.
Anyway, both approaches are correct, but the second approach (adding the rates) is better than the first (working together formula), in my opinion. Several reasons:
1) There are fewer steps in the calculation.
2) The calculation steps themselves are easier (450/5.5 = 4500/55 = 900/11 is much better than 1/75 - 1/900 = 12/900 - 1/900 = 11/900 = 1/A, therefore A = 900/11) In fact, your explanation for the first approach threw me because I think there is an error/typo in it: 1/A does not equal 1/81 exactly--looks like you might have been approximating because the calculation was such a pain!
3) They give you the rates outright--you can immediately combine them, no preliminary calculations required.
You might note that the "working together formula" and "adding the rates to get the combined rate" are the same thing--the formula is based on adding the rates. So what's the distinction? The "working together formula" is more useful for problems in which you don't know one of the individual rates, but are given the combined rate. The "adding the rates" shortcut is most useful on problems (such as this one) in which you know the individual rates and are asked to calculate the total time, or less likely, simply the combined rate.
Emily Sledge
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ManhattanGMAT
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ManhattanGMAT
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