SOLUTION: Two pipes running together can fill a tank in 15 minutes. The larger pipe can fill the tank 16 minutes sooner than the smaller pipe. Find the time in which each pipe alone can fill
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Question 979707: Two pipes running together can fill a tank in 15 minutes. The larger pipe can fill the tank 16 minutes sooner than the smaller pipe. Find the time in which each pipe alone can fill the tank.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two pipes running together can fill a tank in 15 minutes.
The larger pipe can fill the tank 16 minutes sooner than the smaller pipe. Find the time in which each pipe alone can fill the tank.
:
Let x = the time required by the larger pipe
then
(x+16) = time required by the smaller
:
let the completed job = 1 (a full tank)
:
A shared work equation
+ = 1
multiply equation by x(x+16), cancel the denominators and you have
15(x+16) + 15x = x(x+16)
15x + 240 + 15x = x^2 + 16x
Arrange as a quadratic equation on the right
0 = x^2 + 16x - 30x - 240
x^2 - 14x - 240 = 0
Factors to
(x-24)(x+10) = 0
positive solution
x = 24 minutes the time of the larger pipe
then
24 + 16 = 40 min for smaller pipe
:
;
See if that checks out
+ =
.625 + .375 = 1
:
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