Question

A motorist travels to a place 150 km away at an average speed of 50 km / hr and returns at 30 km / hr . His average speed for the whole journey in km / hr is ?

Answer 1

$\underline{\underline{\Huge{\textbf{Solution:}}}}$

Given,
A motorist travels to a place 150 km away at an average speed of 50 km / hr and returns at 30 km / hr .



$\underline{\huge{\textsf{Step-1:}}}$
Find the Total distance covered by motorist

Distance covered by the motorist is the sum of distance from the start point to the place and the place to the start point.

$\implies Total\: Distance\: covered = 150\: km+150\: km$ ————[1]

$\implies Total\: Distance\: covered = 300\: km$



$\underline{\huge{\textsf{Step-2:}}}$
Find the time taken by the motorist to reach the place from start point

We have,
$\bigstar\: \mathbf{time\: taken = \dfrac{Distance}{Speed}}$

time taken to reach the place from start point =$\dfrac{150}{50}$

$\implies$ time taken to reach the place from start point = 3 s



$\underline{\huge{\textsf{Step-3:}}}$
Find the time taken by the motorist to reach the start point from place

We have,
$\bigstar\: \mathbf{time\: taken = \dfrac{Distance}{Speed}}$

time taken to reach the start point from place =$\dfrac{150}{30}$

$\implies$ time taken to reach the start point from place = 5 s



$\underline{\huge{\textsf{Step-4:}}}$
Find the total time taken by the motorist

Total time taken by the motorist is the sum of time taken to reach place and return to starting point .

$\implies$ total time taken = time taken to reach place from starting point + time taken to reach the starting point from place

$\implies total\: time\: taken = 3 s + 5 s$

$\implies total\: time\: taken = 8 s$ ————[2]



$\underline{\huge{\textsf{Step-5:}}}$
Find the Average speed

We have,
$\bigstar\: \mathbf{Average\: Speed = \dfrac{Total\: Distance}{Total\: time\: taken}}$

Substituting [1] & [2]

$\implies Average\: Speed = \dfrac{300}{8}$

$\implies Average\: Speed = \dfrac{75}{2}$

$\implies Average\: Speed = 37\, \dfrac{1}{2}$

$\implies Average\: Speed = 37.5\: kmph$


$\therefore$
$\blacksquare\: \textsf{Average Speed of the Motorist is \underline{\large{\textbf{37.5\: kmph}}}}$