SOLUTION: Word Problem. Solve the problem. Two pipes can fill a large tank in 10 hours. One of the pipes, used alone, takes 15 hours longer than the other to fill the tank. How long would e

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Question 311925: Word Problem. Solve the problem.
Two pipes can fill a large tank in 10 hours. One of the pipes, used alone, takes 15 hours longer than the other to fill the tank. How long would each pipe take to fill the tank alone? Show your work.
Found 3 solutions by stanbon, mananth, josmiceli:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website!
Two pipes can fill a large tank in 10 hours. One of the pipes, used alone, takes 15 hours longer than the other to fill the tank. How long would each pipe take to fill the tank alone?
-------------------------------------------
Together Data:
time = 10 hrs/job ; rate = 1/10 job/hr
-----------------------------------------
One-Pipe Data:
time = x+15 hrs/job ; rate = 1/(x+15) job/hr
------------------
Other-Pipe Data:
time = x hrs/job ; rate = 1/x job/hr.
==========================================
Equation:
rate + rate = together rate
1/x + 1/(x+15) = 1/10
----
10(x+15) + 10x = x(x+15)
20x + 150 = x^2 + 15x
--------------------------
x^2 - 5x - 150 = 0
(x-15)(x+10) = 0
Positive solution:
x = 15 hrs (time for one of the pipe)
x+15 = 30 hrs (time for the other pipe)
==============================================
Cheers,
Stan H.

Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website!
Let filling the tank be 1 job.
two pipes do the job in 10 hours
they do 1/10 of the job in 1 hour
.
one pipe alone does in x hours.
so it does 1/x of the job in 1 hour.
.
the other pipe does in x+15 hours
so it does 1/ x+15 of the job in 1 hour
.
1/x + 1/ x+15 = 1/10
x+15+x / x(x+15) = 1/10
2x+15 /x(x+15)= 1/10
10(2x+15)=x(x+15)
20x+150=x^2+15x
x^2+15x-20x-150=0
x^2-5x-150=0
x^2-15x+10x-150=0
x(x-15)+10(x-15)=0
(x-15)(x+10)=0
x=15
one pipe does it in 15 hours
the other does it in 30 hours
..

Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website!
Let = time it takes one pipe to fill tank in hrs
Then = hrs other pipe takes to fill tank
Add the rates of each pipe to fill tank to get
the rate of both filling tank together
(1 tank/x hrs) + (1 tank/x + 15 hrs) = (1 tank/10 hrs)

Multiply both sides by

Use quadratic formula

(there is a (-) answer, but I can't use it

One pipe takes 15 hrs
the other pipe takes 30 hrs
check:

multiply both sides by

OK