Problem Solving

BTGmoderatorLU wrote:Source: Veritas Prep

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

The OA is D

Working together hoses A and B will fill 1/6 + 1/4 = 5/12 part of the pool

Thus, they together can fill completely in 12/5 hours

Given that they together filled half the pool, they would work for 1/2 of 12/5 = 6/5 hours

Part of the work done by hose B during that period = 1/4*6/5 = 3/10 part

Once half the pool is filled, only hose B fills the remaining half part; thus, part of the pool filled by hose B = 3/10 + 1/2 = 8/10 = 4/5

The correct answer: D

Hope this helps!

-Jay
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BTGmoderatorLU wrote:Source: Veritas Prep

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

The OA is D

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