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.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> 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.       Log On


   

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) About Me  (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
%28%28b-3%29%29%2F4 + %28%28b-3%29%29%2Fb = 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
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
in this equation, x=b; a=1; b=-3; c=-12
b+=+%28-%28-3%29+%2B-+sqrt%28-3%5E2-4%2A1%2A-12%29%29%2F%282%2A1%29+
:
b+=+%283+%2B-+sqrt%289+-%28-48%29%29%29%2F2+
:
b+=+%283+%2B-+sqrt%2857%29%29%2F2+
the positive solution is what we want here
b+=+%283+%2B+7.55%29%2F2+
b = 10.55%2F2
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)
2.275%2F4 + 2.275%2F5.275 =
.56875 + .43128 = 1.000; confirms our solution