Math CentralQuandaries & Queries


Question from Mubashir, a student:

Steven left Town A and walked towards Town B at a speed of 100m/min. At the same time, Jason and Melvin started from Town B and walked towards Town A at a speed of 80m/min and 75m/min respectively. If Steven met Melvin six minutes after passing Jason, find the distance between Town A and Town B.


The important fact here is that rate is distance over time. You are measuring distance in meters and time in minutes so the rate is in meters/minutes.

Suppose the distance between A an B is $d$ meters. I am going to look at Steven and Jason. At what rate is the distance between them decreasing? I am going to call this rate $r_1$ m/min. Suppose $t_1$ is the time when they meet. At this time they have travelled $d$ meters. hence

\[r_1 = \frac{d}{t_1}.\]

Write a similar equation for Steven and Melvin where $t_2$ is the time when they meet. What do you know about $t_2$ and $t_1$?

Solve for $d.$


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