SOLUTION: Alice can vacum in 40 minutes. It takes Bob 45 minutes to do the same job. Find the time it takes Alice and Bob to do the job together.

Question 685057: Alice can vacum in 40 minutes. It takes Bob 45 minutes to do the same job. Find the time it takes Alice and Bob to do the job together.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x = amount of time it takes both working together to vacuum the job
Alice vacuums at the rate of 1/40 of the job per min
Bob vacuums at the rate of 1/45 of the job per min
Together they vacuum at the rate of 1/40 + 1/45=9/360 + 8/360=17/360 of the job per min
Soooooo
(17/360)*x=1 (one vacuum job, that is)
x=360/17=~~~~~21.2 min
CK
In 360/17 min, Alice vacuums (1/40)*(360/17)=9/17 of the job
In 360/17 min Bob vacuums (1/45)*(360/17)=8/17 of the job
9/17 + 8/17=17/17=the job
Hope this helps--ptaylor
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