Question

Please help! A jogger runs at a speed of 4 m/s for 600s, slows to 3 m/s for the next 400s and then travels the final 800s at a speed of 2.5 m/s. What is the average speed of the jogger?

Answer 1

Given data:

A jogger runs at a speed of v_1=4 m/s for t_1=600 s.

Again he runs at speed of v_2=3 m/s for t_2=400 s.

Again he runs at speed of v_3=2.5 m/s for t_3=800 s.

The distance is given as,

`s=v* t`

The distance traveled by the jogger is 600 s is given as,

`\begin{gathered} s_1=v_1* t_1 \\ =(4\text{ m/s})*(600\text{ s}) \\ =2400\text{ m} \end{gathered}`

The distance traveled by the jogger in the next 400 s is given as,

`\begin{gathered} s_2=v_2* t \\ =(3\text{ m/s})*(400\text{ s}) \\ =1200\text{ m} \end{gathered}`

The distance traveled by the jogger in the last 800 s is given as,

`\begin{gathered} s_3=v_3* t \\ =(2.5\text{ m/s})*(800\text{ s}) \\ =2000\text{ m} \end{gathered}`

The average speed is given as,

`\begin{gathered} v_(avg)=\frac{\text{ total distance traveled}}{\text{ total time taken}} \\ =(s_1+s_2+s_3)/(t_1+t_2+t_3) \\ =\frac{(2400\text{ m})+(1200\text{ m})+(2000\text{ m})}{(600\text{ s})+(400\text{ s})+(800\text{ s})} \\ \approx3.11\text{ m/s} \end{gathered}`

Therefore, the average speed of the jogger is 3.11 m/s.