SOLUTION: Working alone, it takes Jake 5 minutes longer to wash the dishes than it takes Mary when she washes the dishes alone. Washing the dishes together, Jake and Mary can finish the job

Question 906351: Working alone, it takes Jake 5 minutes longer to wash the dishes than it takes Mary when she washes the dishes alone. Washing the dishes together, Jake and Mary can finish the job in 6 minutes. How long does it take Mary to wash dishes by herself?
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
1/x+1/(x+5)=1/6
(6*x*(x+5))/x+(6*x*(x+5))/(x+5)=(6*x*(x+5))/6
(6*(x+5))+6*x=x*(x+5)
6*x+30+6*x=x^2+5*x
12*x+30=x^2+5*x
x^2-7*x-30=0
x^2-7*x=30
add it
x^2-7*x+(-7/2)=30+(-7/2)
square it
x^2-7*x+(49/4)=30+(49/4)
x^2-7*x+(12.25)=30+(12.25)
x^2-7*x+(12.25)=42.25
(x-3.5)^2=42.25
(x-3.5)^2=42.25
x-3.5=+-6.5
x=3.5+6.5
One answer is x=10 y=15
Mary can do them alone in 10 minutes
Jake can do them alone in 15 minutes
check
1/10+1/15=1/6
3/30+2/30=5/30
5/30=5/30
ok
Another answer
x=3.5-6.5
Another answer is x=-3.0
For real life cases involving time, distance and other measurements, we reject the negative results.

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