Running on an escalator
Algebra
Level
3
Johnny ran up an escalator going up and took 30 steps to reach the top. He then foolishly ran down the same escalator and took 70 steps to reach the bottom. How many steps would he need to run up or down the escalator if it was stationary? He runs at the same speed each time.
The answer is 42.
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1 solution
The number of steps taken is proportional to the time taken for each run, and the total speeds at which he moves are inversely proportional to the times he takes. These total speeds are of course his own running speed plus or minus the speed of the escalator; so his running speed is the mean of the two total speeds. Thus, if he would take n steps when the escalator is stationary, 1/n is the mean of 1/30 and 1/70, which works out as 1/42, making n = 42.