Question

The time needed for a 15 miles long hike depends on the average speed of the hiker. Write the formula that describes this time as the function of the average speed.

Answer 1

T(r) = 15/r

We start out with the formula for distance, d = rt, where d is the distance, r is the rate (speed), and t is the time.  We know the distance is 15 miles:

15 = rt

We want this as a function of the speed; this means we want speed to be the independent variable and time to be the dependent.  We cancel the r away from t by dividing:

15/r = rt/r
15/r = t

Now we write it in function notation:
t(r) = 15/r