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Speeding Chickens

Continuing with the theme of a speeding car......

Known Fact: The distance a speeding car takes to stop is directly proportional to the square of the car's speed when the brakes are first applied.

Police Report: Two teenage drivers (driving identical Supra-Fords) were playing chicken by driving towards each other and waiting to apply the brakes at the last instant. According to our data chart, a Supra-Ford requires 180 feet to stop if it's brakes are applied at a speed of 60 miles/hour. According to the skid mark patterns, the drivers applied their brakes simultaneously when the cars were 300 feet apart, stopping with only 10 feet separating their cars. Plus, according to street observers, one car was traveling twice the speed of the other.

Question: What were the respective speeds of the two Supra-Fords just before they put on their brakes?

Related Question of Interest: What would have happened if each car was driving 5 mph faster?


Source: Adapted from Ethan Bolker's Using Algebra, 1983, p. 239

Hint: Go back and review last week's problem.


Solution Commentary: Sorry, you are on your own here....you can do it with a little more algebra.