Question 312697
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.
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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
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Together they empty the tank in 12 minutes
They do 1/12 of the job in 1 minute.
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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
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Jill takes 20 minutes
Jack takes 30 minutes
So x= 20 a positive number