Question

The loser of the above race had to run an extra 1600 m as terms of a bet. She runs the first 800 m at an average speed of 6 m/s and the next 800 m at an average speed of 8 m/s.
a. What is her total time needed to run 1600 m?
b. What is her average speed?

Answer 1

a. 233.3 s

First, we calculate the time the runner needs to cover the first 800 m:

$t_1 = \frac{d_1}{v_1}$

where

$d_1 = 800 m$

$v_1 = 6 m/s$ is the speed in the first part

Substituting,

$t_1 = \frac{800}{6}=133.3 s$

Similarly, the time needed to cover the second part was

$t_2 = \frac{d_2}{v_2}=\frac{800}{8}=100 s$

So the total time the runner needed to finish the race was:

$t=t_1 + t_2 = 133.3 s + 100 s = 233.3 s$

b. 6.86 m/s

The average speed can be calculated as follows:

$v=\frac{D}{t}$

where

$D=d_1 + d_2 = 800+800 = 1600 m$ is the total length of the race

t = 233.3 s is the time taken

Substituting,

$v=\frac{1600}{233.3}=6.86 m/s$