Math CentralQuandaries & Queries


Question from Laura, a teacher:

At 11:00 a.m., Jake started driving along a highway at constant speed of 50 miles per hour. A quarter of an hour later, Sara started driving along the same highway in the same direction as Jake at the constant speed of 65 miles per hour. At what time will Sara catch up with Jake

Hi Laura,

For this type of question I often think of a moving sidewalk at an airport. The sidewalk moves at a constant rate and you can stand on it and move at that rate.

moving sidewalk
Image from atmtx

Suppose that the sidewalk is moving at 50 miles per hour when Jake steps on at 11:00 am. He stands still for a quarter of an hour so he has moved a quarter of 50 or 12.5 miles. At this time, 11:15 am, Sara steps onto the sidewalk and walks at 15 miles per hour. You are standing off to the side and from your vantage point Jake is 12.5 miles ahead of Sara, moving at 50 miles per hour and Sara is moving at 65 miles per hour. From Sara's point of view Jake is 12.5 miles ahead of her, standing still and she is travelling at 15 miles per hour. How long will it take for her to travel 12.5 miles to catch up to Jake? What is the time then?

It's unrealistic to think that a moving sidewalk is moving at 50 miles per hour but I hope the analogy helps,

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