Answer: Hello there!
We know that the race is 5 kilometers long and that the runner runs 1 kilometer every 3 minutes.
Now we want to know the distance to the finish line after x minutes.
if we define the position zero as the starting point of the race; then the positon equation of the student as a function of x, where x is minutes, is:
p(x) = (1/3)km/min * x
where at x = 0, his position is 0 (so he is in the starting point of the race)
we know that the finish line is at a distance of 5 kilometers from the starting point, then the distance between the student and the finish line can be written as:
d(x) = 5 km - (1/3)km/min*x
now you can replace the number x whit the number of minutes that the student has been running, and you can find the distance left to finish the race.
Whit this equation you also can valuate d(x) in 0 ( this means that the distance to the finish line is 0 km)
And find the time needed in order to finish the race:
d(x) = 0 = 5km - (1/3)km/min*x
x = 5*3 min = 15 min
