A student is running a 5-kilometer race. He runs 1 kilometer every 3 minutes. Select the function that describes his distance from the finish line after x minutes.

Answer 1

The total distance of the race is 5 km. The student runs 1 km every 3 minutes.

The equation can be modeled as y = mx + c, with m (slope) equal to the speed. The independent value, x, is time and the dependent value, y, is distance. Speed is modeled as distance/time, so in this case, speed is 1 km/3 minutes.

This then brings the equation to y = (1/3)x + c. We know that with time = 0, the distance will remain 5 km. 5 = (1/3)(0) + c, and therefore c = 5.

This then makes the equation y = (1/3)x + 5. As a final step, we must revisit the slop to see if the slop should be positive or negative. Since as time goes on, we expect the distance of the race left to become smaller, therefore the slope should be negative.

This yields the final equation: y = -(1/3)x +5.

Answer 2

1. The rate at which the student runs is 1 km per 3 minutes. This same as 1/3 km per minute
2. x(1/3 km/m) ... if x is the number of minutes the student runs, the this expression give the distance (in km) from the starting line after x minutes. Thus, the distance from the finish line is this expression subtracted from 5 km
3. Thus, distance from finish line = 5 km - x(1/3 km/m) or d = 5 - x/3 (km)