SOLUTION: Two taps A & B altogether fill a swimming pool in 15 hrs. Taps A & B are kept open for 12 hrs & then Tap B is closed. It takes another 8 hrs for the swimming pool to be filled. How

Question 896484: Two taps A & B altogether fill a swimming pool in 15 hrs. Taps A & B are kept open for 12 hrs & then Tap B is closed. It takes another 8 hrs for the swimming pool to be filled. How many hours does each tap requires to fill the swimming pool.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let A equal the rate of tap A.
let B equal the rate of tap B.

when they work together their rates are additive.

the formula to use is R*T = Q

Q = 1 which represents 1 full pool.

T = 15

R = A+B

formula becomes:

(A+B)*15 = 1

you can solve for (A+B) to get:

(A+B) = 1/15

that's the combined rate when both pipes are open.

now you run both pipes for 12 hours.

since R*T = Q, your formula becomes:

(A+B)*12 = x

Q is equal to x because we don't know what it is yet.

but we do know that (A+B) = 1/15, so we get:

1/15 * 12 = x which results in x = 12/15 which can be simplified to x = 4/5.

the both pipes can fill 4/5 of the pool in 12 hours.

that leaves 1/5 of the pool still needing to be filled.

since pipe B is closed, pipe A has to finish the job.

the formula is still R*T = Q

this time Q = 1/5 and T = 8 and R = A only because B is closed.

the formula becomes:

8*A = 1/5

solve for A to get A = 1/40

that's the rate of pipe A.

pipe A can fill 1/40 of the pool in one hour.

now we want to know the rate of pipe B.

since we know that A+B = 1/15 and we know that A = 1/40, we can substitute in this equation to find B.

the formula becomes:

1/40 + B = 1/15

subtract 1/40 from both sides of this equation to get:

B = 1/15 - 1/40 which is equivalent to:

B = 8/120 - 3/120 which is equal to 5/120 which is equal to 1/24.

we now have the individual rates.

A = 1/40
B = 1/24

pipe A will take 40 hours to fill the pool by itself.
pipe B will take 24 hours to fill the pool by itself.

working together, the formula becomes (A+B)*15 = 1

replace A and B with their respective values and you get:

(1/40 + 1/24) * 15 = 1

solve to get:

1 = 1 which confirms the solutions are good.

12 hours working together fills 4/5 of the pool and then pipe A takes over for the remaining 1/5 of the pool working at 1/40 of the pool per hour.

1/40 * 8 = 8/40 = 1/5.

solution is confirmed.

rates are:

A = 1/40 of the pool per hour.
B = 1/24 of the pool per hour.

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