SOLUTION: If it takes 2 days for 5 workers to finish painting a wall at a rate of 6 hours per day, then how long will it take 7 workers to finish painting a wall at a rate of 7 hours per day

First of all 2 days at 6 hours per day is 12 hours.

So first of all we'll pretend the problem just speaks of hours like this:

The least common multiple of 5 workers and 7 workers is 35 workers.

35 workers is 7 times 5, so 35 workers can finish painting 7 walls in 12 hours.

7 workers is only  as many as 35, so it will take 7 workers 5 times as long
or 60 hours to paint 7 walls.  So to paint only 1 wall will take only th as
long as it takes to paint 7 walls.  th of 60 hours is or  or  hours.  
So they'll work 1 7-hour day and will finish after  hours on the
second day.

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You can also use the worker-time-job formula, which is:



where

W1 = the number of workers in the first situation.
T1 = the number of time units (hours in this case) in the first situation.
J1 = the number of jobs in the first situation.

W2 = the number of workers in the second situation.
T2 = the number of time units (hours in this case) in the second situation.
J2 = the number of jobs in the second situation.

W1 =  5             W2 = 7     
T1 = 12             T2 = the unknown quantity 
J1 =  1             J2 = 1









 hours.  So they'll work 1 7-hour day and will finish after
 hours on the second day.

Edwin