SOLUTION: It takes Jake 5 minutes longer to wash the dishes than it takes Adrienne when she washes the dishes alone.l Washing the dishes together, Jake and Adrienne can finish the job in 6

Question 247592: It takes Jake 5 minutes longer to wash the dishes than it takes Adrienne when she washes the dishes alone.l Washing the dishes together, Jake and Adrienne can finish the job in 6 minutes. How long does it take Jake to wash the dishes by himself?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
It takes Jake 5 minutes longer to wash the dishes than it takes Adrienne when she washes the dishes alone.
l Washing the dishes together, Jake and Adrienne can finish the job in 6 minutes.
How long does it take Jake to wash the dishes by himself?
:
Let t = time for J to do it alone
then
(t-5) = time for A to do it alone
:
Let the completed job = 1
:
+ = 1
Multiply by t(t-5), results
6(t-5) + 6t = t(t-5)
:
6t - 30 + 6t = t^2 - 5t
:
12t - 30 = t^2 - 5t
Arrange as a quadratic equation
0 = t^2 - 5t - 12t + 30
:
t^2 - 17t + 30 = 0
Factors to
(t-15)(t-2) = 0
Two solutions
t = 15 min, J alone, this one makes sense, the other one doesn't
;
:
Check solution
6/10 + 6/15 =
.6 + .4 = 1
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