SOLUTION: jack and jill are hired to empty a tank. if they work together it takes them 12 minutes. working alone, jack would take ten minutes longer thank jill to empty the tank. how long do

Question 312697: jack and jill are hired to empty a tank. if they work together it takes them 12 minutes. working alone, jack would take ten minutes longer thank jill to empty the tank. how long does it take for jack to empty the tank by himself? how long does it take jill?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
let emptying 1 tank = 1 job
let jill take x minutes to empty the tank.
so she does 1/x of the job in 1 minute.
..
Jack takes 10 minutes more than jill
so he takes x+10 minutes to empty the tank.
so he does 1/ x+10 of the job in 1 minute
..
Together they empty the tank in 12 minutes
They do 1/12 of the job in 1 minute.
..
1/x + 1/ x+10 = = 1/12
LCM = x(x+10)
x+10 +x = x(x+10) /12
12(2x+10)= x^2 +10x
24x+120=x^2 +10x
x^2-14x-120=0
x^2-20x+6x-120
x(x-20)+6(x-20)=0
(x+6)(x-20)=0
..
Jill takes 20 minutes
Jack takes 30 minutes
So x= 20 a positive number
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