SOLUTION: There are 480 dishes that need to be rinsed. John can rinse them in 80 minutes by himself. It will take his friend Bob 120 minutes to rinse these dishes. How long will it take them

Algebra ->  Equations -> SOLUTION: There are 480 dishes that need to be rinsed. John can rinse them in 80 minutes by himself. It will take his friend Bob 120 minutes to rinse these dishes. How long will it take them      Log On


   

Question 280103: There are 480 dishes that need to be rinsed. John can rinse them in 80 minutes by himself. It will take his friend Bob 120 minutes to rinse these dishes. How long will it take them if they rinse these 480 dishes together?
Found 2 solutions by josmiceli, richwmiller:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The number 480 does not need to enter the calculations
Just call washing that many dishes 1 job
In words:
(John's rate of working) + (Bob's rate of working) = rate of working together
John's rate = 1 job/80 min
Bob's rate = 1 job/120 min
1%2F80+%2B+1%2F120+=+1%2Ft
Multiply both sides by 120t
1.5t+%2B+t+=+120
2.5t+=+120
t+=+48
It will take them 48 minutes working together

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
We have to assume there are two places with easy access to the same dishes and the two workers don't get in each other's way.
Even 80 minutes seem to be excessively long to rinse dishes. We are not talking about washing them but just rinsing them.
x/80+x/120=1
3x+2x=240
5x=240
x=240/5
x=48 minutes together
another interesting way to calculate using the 480 dishes
in 1 minute john can do 480/80=6 dishes
in 1 minute bob can do 480/120=4 dishes
4x+6x=480
10x=480
x=48 minutes