Question

25. A bus travels the first one-third distance at a speed of
10 km h-1, the next one-third distance at a speed of
20 km h-1 and the next one-third distance at a speed
of 30 km h-1. The average speed of the bus is . answer is 50/11 m /s .please give solution​

Answer 1

Answer:

See below.

Explanation:

Let 'x' bet the total distance travelled by the bus. Time taken is the distance travelled divided by the speed.

Time taken to travel the 1st 1/3 distance,

$\begin{aligned}t_{1}=\dfrac {x}{3}\cdot \dfrac {1}{10}\\ \end{aligned}$

Similarly the time taken to travel the 2nd and 3rd 1/3 distances,

$\begin{aligned}t_{2}=\dfrac {x}{3}\cdot \dfrac {1}{20}\\ t_{3}=\dfrac {x}{3}\cdot \dfrac {1}{30}\end{aligned}$

Average speed is given by,

$\begin{aligned}V=\dfrac {x}{t_{1}+t_{2}+t_{3}}\\ =\dfrac {x}{\dfrac {x}{3}\left( \dfrac {1}{10}+\dfrac {1}{20}+\dfrac {1}{30}\right) }\end{aligned}$

$\begin{aligned}=\dfrac {x}{\dfrac {x}{3}\cdot \dfrac {1}{10}\cdot \dfrac {10}{6}}\\ =18 \ km \ hr^{-1}\end{aligned}$

Which makes 5 m/s.