Answer
$3\frac{3}{7}\ hours$
Work Step by Step
Step 1. Joe will do $1/6$ of the job per hour.
Step 2. Sam will do $1/8$ of the job per hour.
Step 3. Work together, they will do $1/6+1/8=7/24$ of the job per hour.
Step 4. It will take them $24/7=3\frac{3}{7}\ hours$ to do the job.