Pierre competes in the $400$-meter dash for his high school track team. He hopes to compete in the Olympics some day, so he studies data from the Olympic results. A table of the times for the Gold Medal winners is shown at right.

1. In the first Olympics in 1896, the winning time was $54.2$ seconds. What was the average speed of the winning runner?

   Hint (a & b)

   $\text{speed }=\frac{\text{distance}}{\text{time}}$

2. If Pierre wants to set an Olympic record, what time does he need to beat? What speed does that correspond to?

   Answer (b):

   $9.2$ m/s

3. Pierre wants to make a graph of the times and speeds as inspiration for his training. What function can he use to model the speed as a function of the time?

   Answer (c):

   $f(t)=\frac{400}{t}$