SOLUTION: I am stuck on how to solve this problem: "I travel from town A to town B, a distance of two miles, at a rate of 30mph. At what speed should I make the return trip so that my avera

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Question 373648: I am stuck on how to solve this problem:
"I travel from town A to town B, a distance of two miles, at a rate of 30mph. At what speed should I make the return trip so that my average speed for the round trip is 60mph? The answer is NOT 90mph."
How would I go about solving this problem?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
What they are trying to teach you is
that an average is never an average of
2 or more averages or a sum of averages. Always go back
to the basic definition of an average. In this case:
(average speed) = (total distance travelled)/(total time elapsed)
The total distance is 2+%2B+2+=+4 mi
The time for the trip from A to B is 2%2F30+=+1%2F15 hr
Let t = the total time
4%2Ft+=+60
4+=+60t
t+=+1%2F15 hr
This tells me that the return tip has to be made in 0 hrs,
and that says that there is no way to average 60 mi/hr
for the round trip.
Suppose the car was a rocket car and could make the return trip
in 1%2F600000 hr
Now I say that the average speed for the round trip is 60 mi/hr
4%2F%281%2F15+%2B+2%2F600000%29+=+60
4%2F%284%2F60+%2B+2%2F600000%29+=+60
4+=+60%2A%284%2F60+%2B+2%2F600000%29
4+=+4+%2B+2%2F10000
There's no way to average 60 mi/hr
no matter how fast you make the return trip