SOLUTION: Mary and John have both completed a trip up an escalator. John took 15 steps on the way up and took 12 seconds to reach the top. Mary took only 7 steps, and took 18 seconds to reac

Question 1149393: Mary and John have both completed a trip up an escalator. John took 15 steps on the way up and took 12 seconds to reach the top. Mary took only 7 steps, and took 18 seconds to reach the top. How many steps does the escalator have in total?
Answer by greenestamps(13202) (Show Source): You can put this solution on YOUR website!

Let x be the number of steps on the escalator.

Since John took 15 steps while on the escalator, the number of steps the escalator moved during his time on it was x-15; since Mary took 7 steps while on the escalator, the number of steps the escalator moved during her time on it was x-7.

Since the escalator moves at a constant rate, the ratio of the numbers of steps the escalator moved during their trips is the same as the ratio of times spent on the escalator. So

There are 31 steps on the escalator.

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