A car and a cyclist start at 10 A.M. from the same point,...

A car and a cyclist start at 10 A.M. from the same point, headed in the same direction. The average speed of the car is $5 \mathrm{mph}$ more than three times the average speed of the cyclist. In $1.5 \mathrm{h},$ the car is $46.5 \mathrm{mi}$ ahead of the cyclist. Find the rate of the cyclist.

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Key Concepts

Formation and Solution of Linear Equations

Many motion problems involve converting worded scenarios into algebraic expressions or equations. These equations are typically linear, meaning they involve variables raised only to the first power, and can be solved using standard algebraic methods. This process provides a systematic way to determine unknown quantities based on the relationships described in the problem.

Distance-Speed-Time Relationship

This concept refers to the fundamental formula distance = speed × time, which is used to calculate the distance traveled by an object moving at a constant speed. It underpins much of the analysis in motion problems where one of these three quantities is unknown and must be determined based on the other two.

Relative Motion

This key concept deals with comparing the movements of two objects, particularly by considering the difference in their speeds. When objects start from the same point and move in the same direction, the relative speed determines how quickly the gap between them grows. It is crucial for understanding scenarios where one object overtakes another or falls behind.

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