SOLUTION: If M men could do J jobs in 1 day, how many days would it take 5 fewer men to do K jobs?

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Question 947348: If M men could do J jobs in 1 day, how many days would it take 5 fewer men to do K jobs?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Uniform Rates for Doing a Job.
%28rate%29%28time%29=%28job%29

If n agents which work at the same rate of r do a job, the rate is n*r.


M%2Ar%2A1=J, the condition.

Let t be how many days for the M-5 men.
%28M-5%29%2Ar%2At=K.

The system is
system%28Mr%2A1=J%2C%28M-5%29rt=K%29
and the unknown variables are r and t.
The question is, how many more days is t than 1, but you essentially want to solve for t.

First equation gives you r=J%2FM.
Substitute into the second equation.
%28M-5%29%28J%2FM%29%2At=K

t=K%28M%2FJ%29%281%2F%28M-5%29%29

highlight%28t=%28KM%29%2F%28J%28M-5%29%29%29, or you could perform the indicated multiplication in the denominator. Finish by subtracting 1. "How many more day...?"