If I went halfway to a town 60 km away at the speed of 30 km/hour, how fast do I have to go the rest of the way to have an average speed of 60 km/hour over the entire trip?

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Solution:

average speed = total distance / total time

60 = 60 / (1 + 30/r)

60(1+ 30/r) = 60

1 + 30/r = 1

30/r = 0

Which is impossible. (The rate of the second half cannot be 0)