SOLUTION: Mary, Sue and Bill work at a motel. If each worked alone, it would take Mary 10 hours, Sue 8 hours, and Bill 12 hours to clean the whole motel. One day Mary come to work early and

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Mary, Sue and Bill work at a motel. If each worked alone, it would take Mary 10 hours, Sue 8 hours, and Bill 12 hours to clean the whole motel. One day Mary come to work early and       Log On


   

Question 103960: Mary, Sue and Bill work at a motel. If each worked alone, it would take Mary 10 hours, Sue 8 hours, and Bill 12 hours to clean the whole motel. One day Mary come to work early and she had cleaned for two hours when Sue and Bill arrived and three finished the job. How long did they take to finish.?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Mary, Sue and Bill work at a motel. If each worked alone, it would take Mary 10 hours, Sue 8 hours, and Bill 12 hours to clean the whole motel. One day Mary come to work early and she had cleaned for two hours when Sue and Bill arrived and three finished the job. How long did they take to finish.?
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Let t = time it took the 3 of them to finish the job
Let the completed job = 1
:
M came early so she did 2%2F10 of the competed job:
:
M alone + three together = completed job
2%2F10 + t%2F10 + t%2F8 + t%2F12 = 1
:
Multiply equation by a common denominator, 120 would work:
120*2%2F10 + 120*t%2F10 + 120*t%2F8 + 120*t%2F12 = 120(1)
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Cancel out the denominators and you have:
12(2) + 12t + 15t + 10t = 120
:
24 + 37t = 120
:
37t = 120 - 24
:
t = 96/37
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t = 2.6 hrs for the 3 to finish the job
:
Check solution on a calc:
M worked 2 + 2.6 = 4.6 hrs:
Mary + Sue + Bill = completed job
4.6%2F10+%2B+2.6%2F8+%2B+2.6%2F12 = 1.00 hrs, confirms our solution
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Did this make some sense to you? Any questions?