SOLUTION: Two pipes can fill a tank in 5 minutes if both are turned on. If only one is used, it would take 39 minutes longer for the smaller pipe to fill the tank than the larger pipe. How

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Two pipes can fill a tank in 5 minutes if both are turned on. If only one is used, it would take 39 minutes longer for the smaller pipe to fill the tank than the larger pipe. How       Log On


   

Question 1060805: Two pipes can fill a tank in 5 minutes if both are turned on. If only one is used, it would take 39 minutes longer for the smaller pipe to fill the tank than the larger pipe. How long will it take for the smaller pipe to fill the tank? (Round your answer to the nearest tenth.)
Found 2 solutions by josgarithmetic, Boreal:
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
WHICH PIPES       RATE AS TANK%2FMINUTES

BIG PIPE             1%2Fx

SMALL PIPE          1%2F%28x%2B39%29

COMBINED PIPES      1%2F5

The question really asks for x%2B39, time for the smaller pipe to fill the tank, if operating alone.

1%2Fx%2B1%2F%28x%2B39%29=1%2F5
Can you now solve this? You will obtain a quadratic equation in the process.

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
x=time it takes for the larger pipe
1/x is fraction of tank for larger pipe per minute.
x+39 is smaller pipe's time
1/(x+39) is its time per minute
(5/x)+5/(x+39)=1, since they fill it in five minutes
5(x+39)+5x=x(x+39) multiplying through by x(x+39)
5x+195+5x=x^2+39x
x^2+29x-195=0
x=(1/2)(-29+ sqrt (841+780)); sqrt (1621)=40.26, use positive root only
x=(1/2)(11.26)=5.6 minutes for larger
44.6 minutes for smaller ANSWER
(1/5.6)+(1/44.6)=0.1785+0.0224=0.2009 of tank in a minute, which is close to 0.2 (rounding error). That is per minute and the whole tank in 5 minutes.