Question

Two taps $A$ and $B$ 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 $8$ day for the swimming pool to be filled. How many days does each tap require to fill the swimming pool?

Answer 1

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.