SOLUTION: word problem from chapter on quadratic equations: Pipe A can fill a tank in 4 hrs. If pipe B works alone, it takes 3 hrs longer to fill the tank than if both pipes work together.

Question 318665: word problem from chapter on quadratic equations: Pipe A can fill a tank in 4 hrs. If pipe B works alone, it takes 3 hrs longer to fill the tank than if both pipes work together. How long will it take for pipe B to fill the tank if it works alone?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Pipe A can fill a tank in 4 hrs. If pipe B works alone,
it takes 3 hrs longer to fill the tank than if both pipes work together.
How long will it take for pipe B to fill the tank if it works alone?
;
Let b = time required by pipe B working alone
then
(b-3) = time required when A & B are working together
:
Let the completed job = 1 (a full tank)
:
A shared work equation
+ = 1
multiply by 4b, results:
b(b-3) + 4(b-3) = 4b
:
b^2 - 3b + 4b - 12 = 4b
Arrange as a quadratic equation
b^2 - 3b + 4b - 4b - 12 = 0
:
b^2 - 3b - 12 = 0
Use the quadratic formula to find b

in this equation, x=b; a=1; b=-3; c=-12

the positive solution is what we want here

b =
b = 5.275 hrs is the time for B to fill the pool alone
:
:
see if that's true, (2.275 hrs for both working together)
+ =
.56875 + .43128 = 1.000; confirms our solution
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