Question 252745
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?
:
let r = the average rate for the round trip
:
Write a time equation: time = {{{dist/speed}}}
time at 10mph  + time at 8 mph = round trip time
{{{x/10}}} + {{{x/8}}} = {{{2x/r}}}
:
Multiply equation by 40r, eliminate all the denominators, results
4rx + 5rx = 40(2x)
4rx + 5rx = 80x
9rx = 80x
Divide both sides by x to eliminate it
9r = 80
r = {{{80/9}}}
r = 8.9 mph is the average for the round trip