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Two hoses (A and B) are filling a pool. Working alone at their individual constant rates Hose A could fill the pool in 6

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by BTGmoderatorDC » Sun Mar 01, 2020 6:55 pm

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Two hoses (A and B) are filling a pool. Working alone at their individual constant rates Hose A could fill the pool in 6 hours, and Hose B could do it in 4 hours. If the two hoses work together until half the pool is full, and then Hose B finishes the pool alone, what fraction of the pool will have been filled by Hose B?


A. 1/2
B. 3/5
C. 3/4
D. 4/5
E. 7/8



OA D

Source: Veritas Prep
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Re: Two hoses (A and B) are filling a pool. Working alone at their individual constant rates Hose A could fill the pool

by Jay@ManhattanReview » Sun Mar 01, 2020 11:32 pm
BTGmoderatorDC wrote: ↑
Sun Mar 01, 2020 6:55 pm
 Two hoses (A and B) are filling a pool. Working alone at their individual constant rates Hose A could fill the pool in 6 hours, and Hose B could do it in 4 hours. If the two hoses work together until half the pool is full, and then Hose B finishes the pool alone, what fraction of the pool will have been filled by Hose B?

A. 1/2
B. 3/5
C. 3/4
D. 4/5
E. 7/8

OA D

Source: Veritas Prep
Since the rate of Hose B (1/4 per hours) is greater than the rate of Hose A (1/6 per hours), part of the half pool filled by Hose B = 1/2 of (6/(6 + 4) = 1/2 of 6/10 = 3/10;

We also know that the remaining half part of the pool is filled by Hose B alone; thus, the fraction of the pool will have been filled by Hose B = 3/10 + 1/2 = 4/5

The correct answer: D

Hope this helps!

-Jay
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Re: Two hoses (A and B) are filling a pool. Working alone at their individual constant rates Hose A could fill the pool

by Scott@TargetTestPrep » Fri Mar 06, 2020 7:53 am
BTGmoderatorDC wrote: ↑
Sun Mar 01, 2020 6:55 pm
 Two hoses (A and B) are filling a pool. Working alone at their individual constant rates Hose A could fill the pool in 6 hours, and Hose B could do it in 4 hours. If the two hoses work together until half the pool is full, and then Hose B finishes the pool alone, what fraction of the pool will have been filled by Hose B?


A. 1/2
B. 3/5
C. 3/4
D. 4/5
E. 7/8



OA D

Source: Veritas Prep
The combined rate of A and B is:

1/6 + 1/4 = 2/12 + 3/12 = 5/12

So the time it takes A and B to do half the pool is:

5/12 x t = 1/2

t = 1/2 x 12/5 = 12/10 = 6/5 hours

Hose A, whose rate is 1/6, has worked for 6/5 hours. Thus, hose A will have completed 1/6 x 6/5 = 1/5 of the pool. Since the rest of the pool will be completed by B, B will have completed 4/5 of the pool.

Answer: D

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