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Rate time problem

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Source: — Problem Solving |
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by GMATGuruNY » Mon Mar 07, 2016 2:24 pm
A pump started filling an empty pool with water and continued at a constant rate until the pool was full. At noon the pool was 1/3 full, and 1 + 1/4 hours later it was 3/4 full. What was the total number of hours that it took the pump to fill the pool?

A. 2 + 1/3
B. 2 + 2/3
C. 3
D. 3 + 1/2
E. 3 + 2/3
Let the capacity of the pool = 12 gallons.

Since the pool is 1/3 full at noon, the amount in the pool at noon = (1/3)(12) = 4 gallons.
Since the pool is 3/4 full 1.25 hours later, the amount in the pool 1.25 hours later = (3/4)(12) = 9 gallons.

Since in 1.25 hours the pump increases the volume from 4 to 9 gallons -- for a total increase of 5 gallons -- the pump's rate = w/t = 5/1.25 = 500/125 = 4 gallons per hour.
Since the pump's rate = 4 gallons per hour, the total time for the pump to fill the 12-gallon pool = w/r = 12/4 = 3 hours.

The correct answer is C.
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by rdds » Thu Mar 10, 2016 12:50 am
Also can the problem be solved this way.
3/4 - 1/3 = 5/12 of the pool is filled in 5/4 or 1.25 hr.
So to fill 1 pool = 5/4 * 12/5 = 3 hrs
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by [email protected] » Thu Mar 10, 2016 10:25 am
didieravoaka wrote:
Please help. Can I have a similar one?

Thanks.
Hi didieravoaka,

Are you looking for additional questions that are similar to this one? I ask because the types of 'rate' questions that you'll see on Test Day are not normally written in the way that this question is written. However, the principal behind all rate questions is basically:

D = R x T

In this prompt, we know that the the TIME was 5/4 hours and we know that the RATE was (3/4 - 1/3 = 5/12 filled per 5/4 hours). Once we convert the data into "how much of the pool was filled per hour", we can answer any question that's asked.

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by Brent@GMATPrepNow » Thu Mar 10, 2016 10:38 am
didieravoaka wrote:
Please help. Can I have a similar one?
How about:
- https://www.beatthegmat.com/two-water-pu ... 84904.html
- https://www.beatthegmat.com/time-to-fill ... 73998.html

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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