Math CentralQuandaries & Queries


Question from Josh:

Marie, a police officer, spots a speeding car and starts chasing it. The speeding car travels at a speed of 130 feet per second. Marie's car reaches a constant speed of 145 feet per second 1725 feet from the start of the chase. During that time, the speeding car has traveled 3150 feet. Write a system of equations to represent this situation.

Hi Josh,

This question is so poorly defined it is difficult to answer. What is it you want to know? At what time does Marie's car reach the 1725 foot mark? How far down the road is it that the Marie catches the speeding car? At what time does Marie catch the speeding car?

I am going to assume that it is the distance or time to catch the speeding car that is important.

Suppose you start your clock at the instant when Marie is at the 1725 foot mark and the speeder is at the 3150 foot mark. Let $DM(t)$ be the total distance that Marie has travelled when your clock reads $t$ seconds. Since Marie travels at 145 feet per second we have that

|\[DM(t) = 1725 + 145 t \mbox{ feet.}\]

Let $DS(t)$ be the total distance that the speeder has travelled when your clock reads $t$ seconds. What is an expression for $DS(t)?$

I hope this helps,

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