Algebra 2 question read description

Question

A roofer requires 16 h to shingle a roof. After the roofer and an apprentice work on a roof for 12 h, the roofer moves on to another job. The apprentice requires 11 more hours to finish the job. How long would it take the apprentice, working alone, to do the job?

Answer 1

This is a shared work problem where each will do a fraction of the work and the two fractions have to add up to 1.

Let's a be the time which the apprentice do the job alone.

Fraction of the job done by roofer is 12/16 and fraction of the job done by apprentice is 23/a. All together they finish the job or

12/16+23/a=1

Solving for a:

23/a=1-12/16

23/a=4/16

a=92