Answer:
50 mi/hr.
Explanation:

Let the speed on the way to the beach = x mi/hr
The time it took to drive to the beach = 5 hours

On their trip home, their speed was 15 mi/hr slower.
• Speed = (x-15) mi/hr
The time it took to drive back home = 6.5 hours

Since the distance to and from the beach is the same, then:

We solve the equation for x:
![\begin{gathered} \text{Open the brackets} \\ 5x=6.5x-97.5 \\ \text{ Subtract 6.5x from both sides of the equation.} \\ 5x-6.5x=6.5x-6.5x-97.5 \\ -1.5x=-97.5 \\ \text{ Divide both sides by }-1.5 \\ (-1.5x)/(-1.5)=(-97.5)/(-1.5) \\ x=65\;(mi)/(hr) \end{gathered}]()
Thus, the speed on the return home will be:

Their speed on the return trip home was 50 mi/hr.