Answer
15.6 hours
Work Step by Step
We are told it takes an experienced roofer 26 hours to roof a house and it takes a beginning roofer 39 hours.
This means in 1 hour, an experienced roofer completes $\dfrac{1}{26}$ of a roof and a beginner completes $\dfrac{1}{39}$ of a roof.
Thus, if they work together, they can complete $\dfrac{1}{26}+ \dfrac{1}{39}$ of a roof in one hour.
Now, we want to find the time it takes them to roof a house together.
So let $t=$the time it takes the two to roof a house together.
Then $\dfrac{1}{t}$ is the fraction of a roof that they can complete in one hour when they work together.
Hence $\dfrac{1}{26}+ \dfrac{1}{39}=\dfrac{1}{t}$.
We multiply both sides by $26*39*t=1014t$ to get $$39t+26t=1014.$$
Now, we solve this for $t$:
$$39t+26t=1014 \\ 65t=1014 \\ t=15.6.$$
Hence, it takes them 15.6 hours to roof a house together.
