Question 750637
A roofer requires 8 h to shingle a roof.
 After the roofer and an apprentice work on a roof for 2 h, the roofer moves on to another job.
 The apprentice requires 16 more hours to finish the job.
 How long would it take the apprentice, working alone, to do the job
:
let a = time required by the apprentice to do the job alone
Let the completed job = 1
:
A typical shared work equation
Each will do a fraction of the job, the two fractions have to add up to 1
The apprentice worked a total 18 hr
{{{2/8}}} + {{{18/a}}} = 1
mult eq by 8a, cancel the denominators and you have
2a + 8(18) = 8a
144 = 8a - 2a
144 = 6a
a = 144/6
a = 24 hrs for the apprentice alone
:
:
Check this
{{{2/8}}} + {{{18/24}}} = 
.25 + .75 = 1