SOLUTION: A large pipe takes 24 hours less to fill a tank than a smaller pipe. If both pipes are turned on it takes 16 hours to fill the tank. How many hours will each pipe take to fill the

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A large pipe takes 24 hours less to fill a tank than a smaller pipe. If both pipes are turned on it takes 16 hours to fill the tank. How many hours will each pipe take to fill the       Log On


   

Question 946571: A large pipe takes 24 hours less to fill a tank than a smaller pipe. If both pipes are turned on it takes 16 hours to fill the tank. How many hours will each pipe take to fill the tank by itself?
Found 2 solutions by josgarithmetic, ptaylor:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
RATES OF PIPES
Large, 1%2F%28x-24%29
Small, 1%2Fx
BOTH, 1%2F16

highlight_green%281%2F%28x-24%29%2B1%2Fx=1%2F16%29

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
A large pipe takes 24 hours less to fill a tank than a smaller pipe. If both pipes are turned on it takes 16 hours to fill the tank. How many hours will each pipe take to fill the tank by itself?
Let x=amount of time it takes small pipe
Then small pipe fills at the rate of 1/x of the tank per hour
x-24=amount of time it takes large pipe
Then large pipe fills at the rate of 1/(x-24) of the tank per hour
With both pipes turned on, they fill at the rate of 1/16 of the tank per hour
Sooooo
(1/x) + 1/(x-24)=1/16 multiply each tem by 16x(x-24)
16(x-24)+16x=x(x-24)
16x-384+16x=x^2-24x
32x-384=x^2-24x
x^2-56x+384=0 quadratic in standard form and it can be factored
(x-8)(x-48)=0
x=8----no good can't have negative hours for large tank
So
x=48 hrs---time it takes small pipe
x-24=48-24=24 hrs time it takes large pipe
CK
(1/48)+(1/24)=???(1/16)
3/48=1/16
1/16=1/16
Hope this helps---ptaylor