Question 380317
Since (average rate) = (total distance)/(total time) we should find the total distance and time traveled.

The cyclist bikes x both ways so (total distance) = 2x. Since the cyclist goes at 10 miles/hr, that means he takes x/10 hours going there, and x/8 hours going back. Therefore,

(total distance)/(total time) = 

{{{(2x)/(x/10 + x/8) = (2x)/(9x/40) = 80/9}}} miles/hr (=8.8889 miles/hr)