SOLUTION: I have one last problem that seems simple enough, but I can't come up with the answer that is given. Could you please show me what I'm missing here? The answer given is: 8.9 , I'm

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Question 252745: I have one last problem that seems simple enough, but I can't come up with the answer that is given. Could you please show me what I'm missing here? The answer given is: 8.9 , I'm thinking 9 . The problem: 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?
Once again, thanks Daniel
Found 2 solutions by Alan3354, ankor@dixie-net.com:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
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?
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d= rt --> t = d/r
t = x/10 + x/8 = 9x/40
r = 2d/t = 2x/t --- 2x for the round trip
r = (2x/1)/(9x/40) = 80x/9x
r = 80/9 = 8.888... mph
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It's not the average, 9 mph, because he spent more time going 8 mph than he did going 10 mph.
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That's the basis of the famous Michelson-Morley experiment that disproved the existence of the "ether" is space.

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
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 =
time at 10mph + time at 8 mph = round trip time
+ =
:
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 =
r = 8.9 mph is the average for the round trip