Two children, who are 224 meters apart, start walking toward...

Two children, who are 224 meters apart, start walking toward each other at the same instant at rates of $1.5 \mathrm{m} / \mathrm{sec}$ and $2 \mathrm{m} / \mathrm{sec},$ respectively (see the figure).
(a) When will they meet?
(b) How far will each have walked?

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Key Concepts

Uniform Linear Motion

This concept refers to movement at a constant speed in a straight line. It establishes that distance traveled is directly proportional to the time of travel when there is no acceleration, which is essential for setting up the equations that relate distance, speed, and time.

Relative Speed

Relative speed is the effective speed between two objects moving either towards or away from each other. In problems where two objects approach one another, their speeds are added together to determine the rate at which the distance between them decreases, simplifying the problem to that of a single moving object covering the total distance.

Algebraic Equation Setup

This involves formulating equations based on the relationship between distance, rate, and time (d = rate × time). By summing the distances covered by each moving object and equating this sum to the total distance, one can solve for the time of meeting or other unknown variables.

Distance Partitioning

After determining the time or combined distance, distance partitioning decomposes the total distance into segments covered by each moving object. Each object’s individual distance is calculated by multiplying its speed by the time, a crucial step for understanding how the total distance is divided between the two participants.

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