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An empty pool being filled with water at a constant rate tak

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An empty pool being filled with water at a constant rate tak [#permalink] New post 25 Jun 2020, 10:50
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Question Stats:

88% (01:01) correct 11% (01:20) wrong based on 9 sessions
An empty pool being filled with water at a constant rate takes 8 hours to fill to 3/5 of its capacity. How much more time will it take to finish filling the pool?

(A) 5 hr 30 min
(B) 5 hr 20 min
(C) 4 hr 48 min
(D) 3 hr 12 min
(E) 2 hr 40 min
[Reveal] Spoiler: OA

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Re: An empty pool being filled with water at a constant rate tak [#permalink] New post 25 Jun 2020, 10:50
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Re: An empty pool being filled with water at a constant rate tak [#permalink] New post 25 Jun 2020, 16:51
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The formula to solve rates questions -> rate * time = work

We know that in 8 hours, we fill the pool to 3/5th capacity or 60% (0.6)
Plug these values in the formula to find the rate
rate * 8 = 0.6
rate = 0.6/8 = 0.075

To completely fill the pool, we need to fill 40% (or 2/5) of its capacity.
Again using our formula,
0.075 * time = 0.4
time = 5.33 hours

However, the answers are given in hours and minutes. 5.33 hours =/= 5 hours and 30 minutes.
we have 5 hours, and 0.33 of an hour. This corresponds to 5 hours and 20 minutes.
Hence, answer choice is B
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Re: An empty pool being filled with water at a constant rate tak [#permalink] New post 26 Jun 2020, 05:29
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Carcass wrote:
An empty pool being filled with water at a constant rate takes 8 hours to fill to 3/5 of its capacity. How much more time will it take to finish filling the pool?

(A) 5 hr 30 min
(B) 5 hr 20 min
(C) 4 hr 48 min
(D) 3 hr 12 min
(E) 2 hr 40 min


IMPORTANT CONCEPT: After 8 hours, 3/5 of the job is finished and 2/5 of the job is remaining.
This means the remaining part of the job is 2/3 the size of the first part of the job.

Think of it this way:
If the pool had a capacity of 5 gallons, then the first part of the job would be filling 3 gallons, and the remaining part of the job is filling 2 gallons.
So, the remaining part of the job (filling 2 gallons) is 2/3 the size of the first part of the job (filling 3 gallons)

So, if it takes 8 hours to do the first part of the job, then the time to do the remaining part = 2/3 of 8 hours
2/3 of 8 hours = 2/3 x 8 hours
= 16/3 hours
= 5 1/3 hours
= 5 hours 20 minutes

Answer: B

Cheers,
Brent
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Re: An empty pool being filled with water at a constant rate tak [#permalink] New post 26 Jun 2020, 09:19
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it takes 8h to fill 3/5
i look for how long it would take to fill entirely the pool - simple cross calculation.

8 x 1 hour = (time for full pool) x (3/5)

time for full pool = (8 x 1 hour) / (3/5)
time for full pool = 8/(3/5)
time for full pool = 8*(5/3) = 40/3 hours

to calculate the time remaining to complete the job, i remove the 8h

40/3 - 8 = (40-24)/3 = 16/3 = 5 hours and 1/3 or 5h20min

answer B
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Re: An empty pool being filled with water at a constant rate tak   [#permalink] 26 Jun 2020, 09:19
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