Question

ii) Two taps A and B can together fill a
swimming pool in 15 days. Taps A and B are
kept open for 12 days and then tap B is
closed. It takes another 8 days for the pool to
be filled. How many days does each tap
require to fill the pool?
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Answer 1

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Answer 2

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Solution:

Let A and B be the rates of the 2 taps.

Equation:

15A + 15B = 1 job

20A + 12B = 1 job

Multiply thru the top equation by 12

multiply thru the bottom equation by 15

180A + 180B = 12

300A + 180B = 15

Subtract and solve for A

120A = 3

A = 1/40 job/day (A's rate)

A would take 40 days to fill the pool alone.

Solve for "B"

20A + 12B = 1

1/2 + 12B = 1

12B = 1/2

B = 1/24 job/day (B's rate)

B would take 24 days to fill the pool alone.