A cyclist bikes x distance at 10 miles per hour and returns over the same path at 8 miles per hour. What is the cyclist’s average rate for the round trip in miles per hour?

Answer 1

It seems to me that you need the average of 10 and 8.
18/2 = 9 mph

Answer 2

No, it's not that simple
Time for first trip = x/10
time for second trip =x/8
distance of total trip = 2x

rate = total distance/total time
=2x/(x/10 +x/8)
=..
=..
=8.88 mph