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

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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) About Me  (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 2%2F3 full? Otherwise, too many unknowns.


Rates, POOLS per HOUR
Slow pipe, 1%2Fx
Fast pipe, 1%2F%28x-24%29
Basic rule for filling a tank, RT=V rate time the volume capacity.


highlight_green%28%281%2Fx%29%2A8%2B%281%2Fx%2B1%2F%28x-24%29%29%2A20=2%2F3%29.
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) About Me  (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 1%2FT of pool in 1 hr, while slower pipe can fill 1%2F%28T+%2B+24%29 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%281%2F%28T+%2B+24%29%29+%2B+20%281%2FT%29+=+2%2F3

28%2F%28T+%2B+24%29+%2B+20%2FT+=+2%2F3

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

84T+%2B+60T+%2B+1440+=+2T%5E2+%2B+48T

144T+%2B+1440+=+2T%5E2+%2B+48T

2T%5E2+%2B+48T+-+144T+-+1440+=+0 

2T%5E2+-+96T+-+1440+=+0

2%28T%5E2+-+48T+-+720%29+=+2%280%29

T%5E2+-+48T+-+720+=+0

(T – 60)(T + 12) = 0 

T, or time faster pipe takes to fill pool is: highlight_green%2860%29 hours	               OR 		   T = - 12 (ignore) 

Time slower pipe takes = 60 + 24, or highlight_green%2884%29 hours

You can do the check!! 

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