Question

A student is running a 10-kilometer race. He runs 1 kilometer every 4 minutes. Select the function that describes his distance from the finish line after x minutes.

A. f(x)=−x+4
B. f(x)=−10x+4
C. f(x)=16x+10
D. f(x)=−x+10

Answer 1

1 km/4 min = 1/4 km per min

f(x) = 10 - (1/4)x

None of the choices are correct.

Answer 2

The correct function for the student's distance from the finish line after x minutes, given a 10-kilometer race and running 1 kilometer every 4 minutes, is D. f(x) = -x + 10.

Step-by-step explanation:

The student in question runs 1 kilometer every 4 minutes. To find out the function that describes his distance from the finish line after x minutes, we need to express his remaining distance in terms of time passed. Since the race is 10 kilometers long, and he runs at a constant speed, the distance he has left to run will decrease linearly over time.

For every 4 minutes that pass, the student runs 1 kilometer, so his speed is 0.25 kilometers per minute (1 km / 4 min). After x minutes, the distance covered will be 0.25x kilometers. Thus, the distance from the finish line can be calculated by subtracting the distance covered from the total distance of the race, which is:

f(x) = 10 - 0.25x

This can be simplified by multiplying the speed by 4 to get rid of the fraction, which gives us:

f(x) = 10 - (1/4)x

To write this in terms of x minutes, you simply multiply x by the fraction representing the speed. Therefore, the correct function is:

D. f(x) = -x + 10