Question 693800
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