### Home > INT3 > Chapter 11 > Lesson 11.2.3 > Problem11-88

11-88.

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?

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

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

$9.2$ 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?

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

 Olympics Time (sec) $\ \ \ \ \$ Olympics Time (sec) 1896 $54.2$ 1960 $44.9$ 1900 $49.4$ 1964 $45.1$ 1904 $49.2$ 1968 $43.8$ 1906 $53.2$ 1972 $44.66$ 1908 $50$ 1976 $44.26$ 1912 $48.2$ 1980 $44.6$ 1920 $49.6$ 1984 $44.27$ 1924 $47.6$ 1988 $43.87$ 1928 $47.8$ 1992 $43.5$ 1932 $46.2$ 1996 $43.49$ 1936 $46.5$ 2000 $43.84$ 1948 $46.2$ 2004 $44$ 1952 $45.9$ 2008 $43.75$ 1956 $46.7$ 2012 $43.94$