SOLUTION: A small swimming pool can be filled with two pipes in three hours. If the larger pipe takes eight hours less to fill the pool, find the time in which it will be filled by each pipe

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Question 331214: A small swimming pool can be filled with two pipes in three hours. If the larger pipe takes eight hours less to fill the pool, find the time in which it will be filled by each pipe singly
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A small swimming pool can be filled with two pipes in three hours.
If the larger pipe takes eight hours less to fill the pool, find the time in
which it will be filled by each pipe singly
:
Let x = time required by the large pipe alone
then
(x+8) = time required by the small pipe alone
:
Let the completed job = 1; (a full pool)
:
3%2F%28%28x%2B8%29%29 + 3%2Fx = 1
Multiply by x(x+8), results
3x + 3(x+8) = x(x+8)
3x + 3x + 24 = x^2 + 8x
Arrange as quadratic equation
0 = x^2 + 8x - 6x - 24
x^2 + 2x - 24 = 0
Factor
(x+6)(x-4) = 0
Positive solution
x = 4 hrs, the large pipe alone
then
4 + 8 = 12 hrs, the small pipe alone
:
:
Check solution
3%2F4 + 3%2F12 = 1; confirms our solution