SOLUTION: Can you help me solve this word problem? Two pipes can fill a large tank in 10 hours. One of the pipes, used alone, takes 15 hours longer than the other to fill the tank. How

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Question 298305: Can you help me solve this word problem?
Two pipes can fill a large tank in 10 hours. One of the pipes, used alone, takes 15 hours longer than the other to fill the tank. How long would each pipe take to fill the tank alone?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two pipes can fill a large tank in 10 hours. One of the pipes, used alone,
takes 15 hours longer than the other to fill the tank.
How long would each pipe take to fill the tank alone?
:
Let x = time for one of the pipes to fill the tank alone
then
(x+15) = time for the other pipe to do it
:
Let the completed job = 1 (a full tank)
:
A typical shared work equation
10%2Fx + 10%2F%28%28x%2B15%29%29 = 1
:
Multiply equation by x(x+15), results:
10(x+15) + 10x = x(x+15)
:
10x + 150 + 10x = x^2 + 15x
:
Arrange as a quadratic equation on the right
0 = x^2 + 15x - 20x - 150
:
x^2 - 5x - 150 = 0
Factors to
(x-15)(x+10) = 0
positive solution
x = 15 hrs is one pipe
and
15 + 15 = 30 hrs is the other pipe
:
:
Check solution in the original shared work equation
10%2F15 + 10%2F30 = 1
.667 + .333 = 1.0