Math CentralQuandaries & Queries


Question from Leria, a student:

The model S= radical 30df describes the relationship between the speed of a car , the conditions of the road, and the length of the skid marks when the car slams on the brakes. S is the speed of the car in miles per hour,
d is the length of the tires' skid marks in feet and f is the coefficient of the friction for the road.

In an accident, a car makes skid marks 85 feet long. The coefficient of friction is 0.6. A witness says that the driver was traveling faster than the speed limit of 35 miles per hour. Can the witness's statement be correct? Use algebra to explain your answer.

A: When trying to solve this problem, I believe that you must use substitution, but I was lost after that. Please help me solve the problem. Thanks.

Hi Leria,

The expression you have is

S = √(30 × d × f) miles per hour.

You also know that d = 85 feet and f = 0.6. Hence

S = √(30 × 85 × 0.6) miles per hour.

Perform the multiplications and then take the square root. Is the value larger than35 miles per hour? Is the witness's statement correct?

I hope this helps,


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