SOLUTION: There are 810 dishes that need to be rinsed. John can rinse them in 90 minutes by himself. It will take his friend Bob 135 minutes to rinse these dishes. How long will it take t

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Question 262841: There are 810 dishes that need to be rinsed. John can rinse them in 90 minutes by himself. It will take his friend Bob 135 minutes to rinse these dishes. How long will it take them if they rinse these 810 dishes together?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
There are 810 dishes that need to be rinsed.
John can rinse them in 90 minutes by himself.
It will take his friend Bob 135 minutes to rinse these dishes.
How long will it take them if they rinse these 810 dishes together?
:
Let t = time required to do the job when they work together
Let the completed job = 1 (the rinsing of 810 dishes)
:
A typical shared work equation
each will do a fraction of the job, the two fractions add up to 1
:
t%2F90 + t%2F135 = 1
multiply equation by 12150 (that's 90*135); results
135t + 90t = 12150
:
225t = 12150
t = 12150%2F225
t = 54 minutes working together
;
:
Check on calc: enter 54/90 + 54/135 = 1; confirms our solution