Particle Moving

A particle moves in a straight line so that its speed is constant for a mile and then changes abruptly for the next mile and is constant for that mile, then changes again, and so on. It moves so that its speed for a given mile varies inversely as the total integral number of miles previously traveled. If the second mile is traversed in 2 hours, how long does it take to travel the nth mile?

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Make a chart.

Now, for that nth mile, d = 1 = rnt.
So 1 =  1  · t, so t = 2(n – 1).
2(n – 1)

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