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Chapter 4: Problem 39

A person walks up a stalled 15 -m-long escalator in \(90 \mathrm{~s}\). When standing on the same escalator, now moving, the person is carried up in \(60 \mathrm{~s}\). How much time would it take that person to walk up the moving escalator? Does the answer depend on the length of the escalator?

Short Answer

Expert verified
It will take the person 36 seconds to walk up the moving escalator. The length of the escalator does not affect this time, as the speeds were calculated independently of it.

Step by step solution

01

Determine the person's walking speed

To find the speed of the person on a stalled escalator, divide the length of the escalator (15 m) by the time taken to walk up it (90 s). This gives a speed of \( 15 \, \mathrm{m} / 90 \, \mathrm{s} = 0.167 \, \mathrm{m/s}\).
02

Determine the escalator's speed

To find the speed of the moving escalator, divide the length of the escalator (15 m) by the time taken to be carried up by it (60 s). This gives a speed of \( 15 \, \mathrm{m} / 60 \, \mathrm{s} = 0.25 \, \mathrm{m/s}\).
03

Determine the combined speed

By adding the person’s speed when walking (0.167 m/s) to the speed of the escalator (0.25 m/s), the combined speed can be found. So, the combined speed is \( 0.167 \, \mathrm{m/s} + 0.25 \, \mathrm{m/s} = 0.417 \, \mathrm{m/s}\).
04

Calculate the time taken to walk up the moving escalator

To find the time taken to walk up the moving escalator, divide the length of the escalator (15 m) by the combined speed (0.417 m/s). So, the time taken is \( 15 \, \mathrm{m} / 0.417 \, \mathrm{m/s} = 36 \, \mathrm{s}\).

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