Question 379528
Let x=amount of time it takes the apprentice, working alone, to complete the repairs
The mechanic works at the rate of 1/3 transmission per hour
The apprentice works at the rate of 1/9 transmission per hour

In 1.5 hours, the mechanic completes (1/3)*1.5  or 1/2 of the job, leaving 1/2 of the job yet to be done. So we have to calculate the following:
(1/9 transmission per hour)* x hours=(1/2 transmission); or
(1/9)x=1/2  multiply each side by 18
2x=9
x=4.5 hours---time required for the apprentice to finish the job

Hope this helps---ptaylor