|
Question 693800: Two pipes can fill a tank in 41 minutes if both are turned on. If only one is used it would take 29 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?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Let x=amount of time it would take the smaller pipe to fill the tank
Then the smaller pipe fills at the rate of 1/x of the tank per min
x-29=amount of time it would take the larger pipe to fill the tank
Then the larger pipe fills at the rate of 1/(x-29) of the tank per min
When both pipes are on, they fill at the rate of 1/41 of the tank per min
So, our equation to solve is:
1/x + 1(x-29)=1/41 multiply each term by 41x(x-29)
41(x-29)+41x=x(x-29) simplify
41x-1189+41x=x^2-29x subtract x^2 from each side and also add 29x to each side
82x+29x-x^2-1189=0 multiply each term by (-1)
x^2-111x+1189=0-----------quadratic in standard form and it cannot be factored exactly but (x-99)(x-12) is certainly close enough to provide a negligible error
So
x=99
and
x=12
12 is not good because this will give a negative value for the larger pipe
x=99 min----------------------time it takes smaller pipe to fill the tank.
Hope this helps---ptaylor
|
|
|
| |
