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,
[tex]s=v\times t[/tex]The distance traveled by the jogger is 600 s is given as,
[tex]\begin{gathered} s_1=v_1\times t_1 \\ =(4\text{ m/s})\times(600\text{ s}) \\ =2400\text{ m} \end{gathered}[/tex]The distance traveled by the jogger in the next 400 s is given as,
[tex]\begin{gathered} s_2=v_2\times t \\ =(3\text{ m/s})\times(400\text{ s}) \\ =1200\text{ m} \end{gathered}[/tex]The distance traveled by the jogger in the last 800 s is given as,
[tex]\begin{gathered} s_3=v_3\times t \\ =(2.5\text{ m/s})\times(800\text{ s}) \\ =2000\text{ m} \end{gathered}[/tex]The average speed is given as,
[tex]\begin{gathered} v_{avg}=\frac{\text{ total distance traveled}}{\text{ total time taken}} \\ =\frac{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}[/tex]Therefore, the average speed of the jogger is 3.11 m/s.
