SOLUTION: Jack and Jill are hired to empty a tank. If they work together it takes them 12 minutes. Working alone, Jack would take 10 minutes longer than Jill to empty the tank. How long does

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Jack and Jill are hired to empty a tank. If they work together it takes them 12 minutes. Working alone, Jack would take 10 minutes longer than Jill to empty the tank. How long does      Log On


   

Question 312902: Jack and Jill are hired to empty a tank. If they work together it takes them 12 minutes. Working alone, Jack would take 10 minutes longer than Jill to empty the tank. How long does it take for Jack to empty the tank himself? How long does it take jill?
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Jack and Jill are hired to empty a tank. If they work together it takes them 12 minutes. Working alone, Jack would take 10 minutes longer than Jill to empty the tank. How long does it take for Jack to empty the tank himself? How long does it take jill?
.
Let x = minutes it takes Jill to do it alone
then
x+10 = minutes it takes Jack to do it alone
.
12(1/x + 1/(x+10)) = 1
multiplying both sides by x(x+10)
12((x+10) + x) = x(x+10)
12(2x+10) = x(x+10)
24x+120 = x^2+10x
120 = x^2-14x
0 = x^2-14x-120
0 = (x+6)(x-20)
x = {-6, 20}
Toss out the negative solution (doesn't make sense) leaving
x = 20 minutes (time it takes Jill)
.
Jack:
x+10 = 20+10 = 30 minutes