A cyclist bikes x distance at 10 miles per hour and returns

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?
A. 8.1
B. 8.3
C. 8.6
D. 8.9 correct answer
E. 9.0
I can\'t figure this out. We have Rate1 x time1 = rate2 x time2, and I can\'t get anywhere with that. Please help!

Solution

The total distanced traveled is 2x.
.
Now, you need the total time traveled.
Applying:
d = rt
or, for us
t = d/r
where
d is distance
r is rate
t is time
.
Time going is
x/10
Time returning is
x/8
Total time is
x/10 + x/8
.
Average speed is
\"total distance\"/\"total time\"
2x/[x/10 + x/8]
cancel out the x\'s:
2/[1/10 + 1/8]
= 2/[8/80 + 10/80]
= 2/[18/80]
= 160/[18]
= 8.9 mph