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Simple Work Problem

Problem Solving — algebra and arithmetic
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by bragot » Fri Mar 26, 2010 3:09 pm
I got this from the Princeton Review Book, but I don't quite understand how they set up the equation:

If Sam can finish a job in 3 hours and Mark can finish a job in 12 hours, in how many hours could they finish the job if they worked together at their respective rates?

A 1
B 2 2/5
C 2 5/8
D 3 1/4
E 4
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by papgust » Fri Mar 26, 2010 7:36 pm
Sam's rate is 1/3, Mark's is 1/12

Together --> 1/3 + 1/12

4/12 + 1/12 = 5/12 [fraction of work done]

Take reciprocal to find the no. of hours,

12/5 = 2 2/5
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by bragot » Fri Mar 26, 2010 7:50 pm
How did you know to take the reciprocal?

Thanks for your help.
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by thephoenix » Fri Mar 26, 2010 8:11 pm
bragot wrote:How did you know to take the reciprocal?

Thanks for your help.
there is a direct formula
if A can do a work in x days and b in y days, then combine they will take (x*y)/(x+y) days
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by MrE2All » Fri Mar 26, 2010 9:01 pm
bragot wrote:How did you know to take the reciprocal?

Thanks for your help.
Their combined rate is 5/12 jobs/hour. They need to complete 1 job. So 5/12 jobs/hr x 12/5 hrs = 1 job.
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