Question 158339
Let x=amount of time it takes the supply pipe to fill the tank when the exhaust pipe is closed
So, the supply pipe fills at the rate of 1/x tank per min

And x+5=amount of time it takes the exhaust pipe to empty the tank
So, the exhaust pipe empties at the rate of 1/(x+5) tank per min

If both are opened, the tank fills at the rate of (1/x)-1/(x+5) tank per min and we are basically told that this equals 1/30 tank per min, so our equation to solve is:

(1/x)-1/(x+5)=1/30  multiply each term by x(x+5)*30
30(x+5)-30x=x(x+5)  get rid of parens
30x+150-30x=x^2+5x  subtract 150 from each side and simplify
x^2+5x-150=0  quadratic in standard form and it can be factored
(x+15)(x-10)=0
x=-15 min------------------------no good!! times in this problem are positive
and
x=10 min----------------------amount of time it takes the supply pipe to fill the tank when the exhaust pipe is closed


CK
(1/10)-(1/15)=1/30
(3/30)-(2/30)=1/30
1/30=1/30
Also

Hope this helps---ptaylor