Math CentralQuandaries & Queries


Question from Larry, a student:

If 3 cars are going 50 mph, and a fourth car pass the first 3 cars in 200 feet, how fast is the fourth car going?

Hi Larry. I think something is missing from your question.

Picture this: Car A is at position 0 feet, Car B is in front of Car A, at position 90 feet (so its front bumper is 90 feet ahead of the front bumper of car A). Car C is at position 180 ft (90 feet in front of Car B's front bumper).

If Car D is just alongside Car A (about to pass it) at position 0 ft, and it passes Car C at position 200 ft, then it has covered 200 feet in the time it took Car C to go 20 feet, so D is going 10 times the speed
of Car C (500 mph !).

However, If the cars are not so spread out, we get different results:
Let's say they are at 0, 25 and 50 feet. Then Car D covers 200 feet in the time Car C goes 150 feet, so car D is going 200/150 x 50 mph = 67 mph.

Without knowing something else, like the time it takes to pass or the spacing of the three cars (I'm assuming of course that the cars are in single-file!) there is no real answer to the question.

Stephen La Rocque

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