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.
:
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
{{{15/x}}} + {{{15/((x+16))}}} = 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
{{{15/24}}} + {{{15/40}}} = 
.625 + .375 = 1
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