Adam S. answered • 03/21/14

Professional and Proficient Math Tutor

By being more efficient by half I assume you mean it takes him half as long.

Y = amount of work to be done in the job.

The rate of work for each man is

A = Y/18.

B = Y/9.

Combining both of their efforts the combined work rate is:

Y/18 + Y/9 = Y/X.

X will be the amount of time it takes for both of the men to complete the work together.

1/18 + 1/9 = 1/X -> 3/18 = 1/X -> X = 18/3 = 6.

It will take 6 days for the men to do the work together.