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Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

The stopping distance of a car is the number of feet that the car travels after the driver starts applying the brakes. The stopping distance of a certain car is directly proportional to the square of the speed of the car, in miles per hour, at the time the brakes are first applied. If the car’s stopping distance for an initial speed of 20 miles per hour is 17 feet, what is its stopping distance for an initial speed of 40 miles per hour?

(A) 34 feet
(B) 51 feet
(C) 60 feet
(D) 68 feet
(E) 85 feet

答案和解析

答案：D

解析：

The stopping distance is directly proportional to the square of the initial speed of the car. If s represents the initial speed of the car, in miles per hour, and d represents the stopping distance, you have that the stopping distance is a function of s and that function d of s = c(s^2), where c is a constant. Since the car’s stopping distance is 17 feet for an initial speed of 20 miles per hour, you know that 17 = c20^2. Therefore, c = 17/20^2 = 0.0425, and the car's stopping distance for an initial speed of 40 miles per hour is 0.042540^2 = 68 feet.