Question 1022956
The rate for A is 1/12 of a project per hour
The rate for B is 1/15 of a project per hour

So if the two work on the project alternating each hour,
the average rate will be (1/12 + 1/15)/2 of a project per hour
or (9/120) per hour
(9/120)X = 1 project
so X = (120/9) = 13 1/3 approximately

More exactly,

Beginning with A and alternating hourly the amount of work completed will be
1/12 + 1/15 + 1/12 + 1/15 + 1/12 + 1/15 + 1/12 + 1/15 + 1/12 + 1/15 +1/12 + 1/15 + 1/12 = 59/60 of a project for 13 hours
The final 1/60 th of the project will be completed at a rate of 1/15 project per hour. (1/15)X = 1/60
Multiply each side by 15 , X =15/60 or 1/4
So the total time is 13 1/4 hours