A pump started filling an empty pool with water and continued at a constant rate until the pool was full. At noon the po

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A pump started filling an empty pool with water and continued at a constant rate until the pool was full. At noon the po

by Gmat_mission » Sat Oct 31, 2020 6:24 am

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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 $$\dfrac13$$ full, and $$1\frac14$$ hours later it was $$\dfrac34$$ full. What was the total number of hours that it took the pump to fill the pool?

A. $$2\frac13$$
B. $$2\frac23$$
C. $$3$$
D. $$3\frac12$$
E. $$3\frac23$$

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Re: A pump started filling an empty pool with water and continued at a constant rate until the pool was full. At noon th

by [email protected] » Wed Dec 01, 2021 2:41 pm
Gmat_mission wrote:
Sat Oct 31, 2020 6:24 am
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 $$\dfrac13$$ full, and $$1\frac14$$ hours later it was $$\dfrac34$$ full. What was the total number of hours that it took the pump to fill the pool?

A. $$2\frac13$$
B. $$2\frac23$$
C. $$3$$
D. $$3\frac12$$
E. $$3\frac23$$

Source: GMAT Prep
For this type of question, I like to assign a "nice value" to the job.

In this case we're looking for a number that works well with 1/3, 3/4 and even 1 1/4
So, let's say the pool has a capacity of 60 liters.

At noon the pool was 1/3 full, . . .
1/3 of 60 liters = 20 liters
So, at 12:00pm, the pool contained 20 liters of water

. . . and 1 1/4 hours later it was 3/4 full.
1 1/4 hours = 1.25 hours = 75 minutes.
3/4 of 60 liters = 45 liters
So, at 1:15pm, the pool contained 45 liters of water

What was the total number of hours that it took the pump to fill the pool?
45 liters - 20 liters = 25 liters
So, in 1.25 hours, 25 liters of water was added to the pool

Rate = output/time
So, the rate at which water is added to the pool = (25 liters)/(1.25 hours) = 20 liters per hour

Time = output/rate
So, at a rate of 20 liters per hour, the time it takes to fill the 60 liter pool = 60/20 liters = 3 hours