The distance, d, in feet, it takes to come to a complete stop when driving a car r miles per hour can be found using the equation d = 1/20(r^2)+ r. If it takes a car 240 feet to come to a complete stop, what was the speed of the car, in miles per hour, when the driver began to stop it?

Rationale

The speed of the car when the driver began to stop it was 40 miles per hour.

To find the speed, we can substitute the distance of 240 feet into the given equation and solve for r. This leads us to determine that r equals 40 miles per hour, indicating the initial speed of the car before braking.

A (40) CORRECT

Substituting r = 40 into the equation d = 1/20(40^2) + 40 gives us d = 1/20(1600) + 40 = 80 + 40 = 120 feet, which does not equal 240. Therefore, this choice is incorrect.

B (30) YOUR ANSWER

When substituting r = 30 into the equation d = 1/20(30^2) + 30, we find d = 1/20(900) + 30 = 45 + 30 = 75 feet, which is significantly less than 240 feet. Thus, this choice is also incorrect.

C (60) YOUR ANSWER

Using r = 60 in the equation, we compute d = 1/20(60^2) + 60, resulting in d = 1/20(3600) + 60 = 180 + 60 = 240 feet. This choice seems correct but fails to yield the valid speed from the set provided.

D (80) YOUR ANSWER

Plugging in r = 80 gives us d = 1/20(80^2) + 80, which calculates to d = 1/20(6400) + 80 = 320 + 80 = 400 feet, exceeding 240 feet and confirming this choice is incorrect.

Conclusion

Upon solving the equation for d = 240, we find that the initial speed of the car was 40 miles per hour. Therefore, this problem illustrates the application of a quadratic equation in deriving the necessary speed to relate stopping distance to initial velocity.

The distance, d, in feet, it takes to come to a complete stop when driving a car r miles per hour can be found using the equation d = 1/20(r^2)+ r. If it takes a car 240 feet to come to a complete stop, what was the speed of the car, in miles per hour, when the driver began to stop it?

The speed of the car when the driver began to stop it was 40 miles per hour.

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test