SOLUTION: Mary, Sue and Bill work at a motel. Working alone, it takes Mary 10 hours, Sue 8 hours, and Bill 12 hours to clean the whole motel. One day Mary came to work 2 hours early and cl

Question 25642: Mary, Sue and Bill work at a motel. Working alone, it takes Mary 10 hours, Sue 8 hours, and Bill 12 hours to clean the whole motel. One day Mary came to work 2 hours early and cleaned until Bill and Sue arrived. How long did it take them to finish the job working together?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Work done = (rate)(time)
Mary work along: =(1/10 job/hr.)(2 hrs.)=1/5 job
Now let the time "they" work together be "x".
Note the phrase "...take them to finish..." can
have two meanings.
It can mean Bill and Sue finished the job, or
it can mean Mary, Bill, and Sue finished the job.
If the 1st you get the following equation:
(1/8)x+(1/12)x=4/5
15x+10x=96
27x=96
x=96/27 hrs. (time Bill and Sue work together to finish the job)
If all three work together for "x" hours:
(1/8)x+(1/12)x+(1/10)x=4/5
15x+10x+12x=96
37x=96
x=96/37 hrs (time Bill and Sue and Mary work together)
Cheers,
Stan H.

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