One machine can turn out 1000 pieces in 12 days.

A second machine takes 18 days to turn out 1000 pieces.

On a particular run the first machine operated for 4 days alone.

The second machine was then put into operation, and the two worked together.

How long did it take to finish 1000 pieces?

:

Let t = time that the two machines worked together

:

Let the completed job = 1 (1000 pieces made)

:

Mach 1 + Mach 2

+ = 1

Multiply eq by 26 to clear the denominators, results:

3(t+4) + 2t = 36

:

3t + 12 + 2t = 36

5t = 36 - 12

5t = 24

t =

t = 4.8 days working together to finish the job

:

:

Check this: (Machine 1 worked 8.8 days)

8.8/12 + 4.8/18 =

.733 + .267 = 1.0

confirms our solution of 4.8 days working together