SOLUTION: One of two pipes can fill a pool 24 hours faster than the other one. The slower pipe filled the pool for 8 hours, then the other pipe was opened. The pipes filled together for 20 h

Question 935598: One of two pipes can fill a pool 24 hours faster than the other one. The slower pipe filled the pool for 8 hours, then the other pipe was opened. The pipes filled together for 20 hours and filled 2/3 of the pool. Find the time that each pipe requires to fill the pool alone. Please help me to solve this complicated problem. I just know that the answer is 60 and 84 hours. But I am really eager to know how to solve it Thank you in advance )))
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39625) (Show Source): You can put this solution on YOUR website!
You mean, 20 hours with the slow tank and then 20 hours with both tanks filled the pool to full? Otherwise, too many unknowns.

Rates, POOLS per HOUR
Slow pipe,
Fast pipe,
Basic rule for filling a tank, RT=V rate time the volume capacity.

.
If you can manage the arithmetic then solving for x is what you want.
Most important is to understand the equation first.
Answer by MathTherapy(10555) (Show Source): You can put this solution on YOUR website!

One of two pipes can fill a pool 24 hours faster than the other one. The slower pipe filled the pool for 8 hours, then the other pipe was opened. The pipes filled together for 20 hours and filled 2/3 of the pool. Find the time that each pipe requires to fill the pool alone. Please help me to solve this complicated problem. I just know that the answer is 60 and 84 hours. But I am really eager to know how to solve it Thank you in advance )))

Let time faster pipe takes to fill pool, be T
Then time slower pipe takes is: T + 24
Thus, faster pipe can fill of pool in 1 hr, while slower pipe can fill of pool in 1 hr
Since slower pipe was turned on for 8 hours, by itself, and for 20 hours, with the faster pipe,
the slower pipe was turned on for a total of 28 (8 + 20) hours
Faster pipe was open for 20 hours
Therefore, we can say that:

28(3)(T) + 20(3)(T + 24) = 2(T)(T + 24) ------- Multiplying by LCD, 3(T)(T + 24)

(T � 60)(T + 12) = 0
T, or time faster pipe takes to fill pool is: hours OR T = - 12 (ignore)
Time slower pipe takes = 60 + 24, or hours
You can do the check!!
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