five friends drove at an average rate of 50 miles per hour t

five friends drove at an average rate of 50 miles per hour to a weekend retreat. On the way home, they took the same route but averaged 75 miles per hour. What was the distance between home and the retreat if the round trip took 10 hours?

Solution

Let t = time it takes to get TO the retreat.
Then 10-t = time it takes to get BACK from the retreat.

Distance to the retreat = Distance back from the retreat
Rate * Time = Rate * Time
50*t = 75(10-t)
50t = 750 -75t
50t+75t = 750
125t=750
t=6 hours to get TO the retreat at 50 mph = 300 miles

As a check, this means that it took only 4 hours to return at 75 mph.
4*75 = 300 miles, and it checks!!