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Up an Escalator

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1. Warren takes the underground train to work and uses an escalator at the railway station. If Warren runs up 6 steps of the escalator, then it takes him 34.5 seconds to reach the top of the escalator. If he runs up 15 steps of the escalator, then it takes him only 21.0 seconds to reach the top.

How many seconds would it take Warren to reach the top if he did not run up any steps of the escalator at all?
Answer: 43.5

Solution:

If he runs up 6 steps, then he needs 34.5 seconds to reach the top.
If he runs up 15 steps, then he needs 21.0 seconds to reach the top.

The 9 additional steps take 13.5 seconds.
Therefore, each step takes 1.5 seconds.

Total steps in escalator = 6 + 34.5 / 1.5 = 29 or Total steps in escalator = 15 + 21.0 / 1.5 = 29.

If Warren did not run up any steps at all,
he would reach the top of the escalator in 43.5 seconds (i.e., 29 steps × 1.5 seconds/step).

Alternative Solution through Equations:

Let the total number of steps in the escalator be x.
The escalator moves at a constant speed given by

Speed of escalator = (x − 6)/34.5 = (x − 15)/21.0

The above equation may be solved as follows.

21.0 (x − 6) = 34.5 (x − 15); or
x = (15 × 34.5 − 6 × 21.0) / (34.5 − 21.0) = 29.

Now, Speed of escalator = (29 − 6)/34.5 = (29 − 15)/21.0 = 1/1.5 steps/second.
Time to reach top = Total Steps / Speed = 43.5 seconds.

Food for thought:

Does it matter whether the escalator is moving up or down?


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puzzle : image for escalator

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