Question 287709
An experienced roofer can roof a house in 26 hours.
 A beginning roofer needs 39 hours to complete the same job.
 Find how long it takes for the two of them to do the job together.
:
Here is how I would do it:
let t = time required for them to complete the job together
:
let 1 = the completed job
:
Each does a fraction of the job, the two fractions add up to 1
:
{{{t/26}}} + {{{t/39}}} = 1
multiply equation by 1014 (that's 26*39), results
39t + 26t = 1014
65t = 1014
t = {{{1014/65}}}
t = 15.6 hrs
:
:
Check solution by find the faction that each does
15.6/26 + 15.6/39 = 
.6 + .4 = 1