SOLUTION: 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

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Question 451180: 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
e) 9.0
I know with averages you add the groups of numbers and then divide by the number of groups. I came up with e)9. I must be missing something because the answer key says that the correct answer is d)8.9. I need to know if the answer key is wrong or if I am doing something wrong. Please show the detailed solution if i am doing something wrong.
Answer by ewatrrr(24785) (Show Source):
You can put this solution on YOUR website!

Hi,
A cyclist bikes x distance at 10 miles per hour
and returns over the same path at 8 miles per hour. (total distance is 2x)
Average rate = total distance/total time:
Note t = D/r t(going) = x/10mph, t(returning) = x/8mph
Average rate =

For ex: If the cyclist went 40mi and biked back...
Average rate = total distance/total time = 80/(40/10 + 40/8) = 80/(4+5) = 80/9