The airport terminal in Geneva, Switzerland has a "moving...

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.

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Key Concepts

Algebraic Problem Solving

This technique involves setting up and solving equations based on known relationships and given data. In problems where multiple scenarios share common variables, equations can be derived for each scenario and then combined to solve for unknown quantities. This method is particularly useful in mechanics problems where differences in movement conditions need to be reconciled algebraically.

Time-Speed-Distance Relationship

This concept relates distance, speed, and time through the equation distance = speed × time. It is fundamental in solving problems where any two of these quantities are known, allowing the third to be calculated. In contexts where an object moves at a constant speed, understanding this relationship helps in setting up equations to determine unknown variables.

Relative Motion

Relative motion describes how the velocity of an object is observed differently from different frames of reference. In problems involving additional motion components, like a moving sidewalk, the effective velocity is the sum of the individual speeds relative to their respective frames. This principle is crucial when calculating the net effect of combined motion, such as a walking speed plus the speed of the moving walkway.

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