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

Algebra ->  Rate-of-work-word-problems -> 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       Log On


   

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) About Me  (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.