SOLUTION: Together two pipes can fill a vat in 9 hours 36 minuters,if the longer pipe takes 8 hours less than the smaller pipe does how long does it take the smaller pipe to fill the vat?

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Question 383941: Together two pipes can fill a vat in 9 hours 36 minuters,if the longer pipe takes 8 hours less than the smaller pipe does how long does it take the smaller pipe to fill the vat?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Together two pipes can fill a vat in 9 hours 36 minutes,
if the longer pipe takes 8 hours less than the smaller pipe.
how long does it take the smaller pipe to fill the vat?
:
Let x = time required by smaller pipe
then
(x-8) = time required by the larger
:
let the completed job = 1; (a full vat)
Change 9 hr 36 min to 9.6 hrs
:
9.6%2Fx + 9.6%2F%28%28x-8%29%29 = 1
Multiply by x(x-8), results:
9.6(x-8) + 9.6x = x(x-8)
:
9.6x - 76.8 + 9.6x = x^2 - 8x
19.2x - 76.8 = x^2 - 8x
combine like terms on the right
0 = x^2 - 8x - 19.2x + 76.8
A quadratic equation
x^2 - 27.2x + 76.8 = 0
Solve this using the quadratic formula
Two solution but only one is reasonable
:
x = 24 hrs is the time required by the smaller pipe
:
:
Check this
9.6/16 + 9.6/24 =
.6 + .4 = 1