Question

A man walks for 45 minutes at a rate of 3 mi/h then jogs for 75 minutes at a rate of 5 mi/h then rests for 30 minutes and finally walks for 90 minutes at a rate of 3 mi/h. Write a piecewise-defined function expressing the distance he traveled as a function of time.

Answer 1

Explanation:

This is a piece-wise function.

The distance function depends on what time period is involved.

From t=0 to t=0.75, the distance function is: .3t

. . By the end of the 45 minutes, he has gone 2.25 miles.

From t=0.75 to t=2, the distance function is: .2.25+5t

. . By the end of the 75 minutes, he has gone another 6.25 miles, a total of 8.5 miles.

From t=2 to t=2.5, the distance function is: .8.5+0t=8.5

. . By the end of the 30 minutes, he hasn't moved; his total is still 8.5 miles.

From t=2.5 to 4, the distance function is: .8.5+3t

. . By the end of the 90 minutes, he has gone another 4.5 miles, a total of 13 miles.

The function would be written like this:

d(t) = 3t 0 ≤ t ≤ 0.75

2.25+5t 0.75≤t<2

8.5 2≤t≤2.5

8.5+3t 2.5<t<4