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Chapter 4: Problem 40

The airport terminal in Geneva, Switzerland has a "moving sidewalk" to speed passengers through a long corridor. Peter, who walks through the corridor but does not use the moving sidewalk, takes \(150 \mathrm{~s}\) to do so. Paul, who simply stands on the moving sidewalk, covers the same distance in \(70 \mathrm{~s}\). Mary not only uses the sidewalk but walks along it. How long does Mary take? Assume that Peter and Mary walk at the same speed.

Short Answer

Expert verified
To find the duration Mary takes, divide the distance of the walkway by the sum of the sidewalk's speed and her walking speed: \( t_m = \frac{d}{v_m} = \frac{d}{v_p + v_{sw}} = \frac{d}{d/150 + d/70} \). The distance \( d \) will cancel out, leaving the time Mary needs to walk the corridor. This requires knowing how to handle fractions and the concept of relative velocities in physics.

Step by step solution

01

Understand the problem and gather data

Three people are mentioned: Peter, who walks, Paul, who simply stands on the moving sidewalk, and Mary, who walks on the moving sidewalk. We know that Peter takes 150 seconds to walk through the corridor and Paul takes 70 seconds to cover the same distance by standing on the sidewalk. It is also stated that Peter and Mary walk at the same speed.
02

Calculate the speeds

If the length of the corridor is \( d \), then Peter's speed \( v_p \) is \( d/150 \) and Paul's speed \( v_{sw} \), the speed of the sidewalk, is \( d/70 \). Mary's speed \( v_m \) is the sum of the sidewalk's speed and her own walking speed, hence \( v_m = v_p + v_{sw} \) or \( v_m = d/150 + d/70 \)
03

Calculate the time Mary takes

We can find the time Mary takes \( t_m \) to cover the same distance by dividing the distance \( d \) by her speed \( v_m \). Hence, \( t_m = d/v_m \). Substitute \( v_m = d/150 + d/70 \) into the equation to solve for \( t_m \).

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Most popular questions from this chapter

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