Simple Work Problem

[bragot]

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

[papgust]

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

[bragot]

How did you know to take the reciprocal?

Thanks for your help.

[thephoenix]

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

[MrE2All]

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.