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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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