Question

A car travels from A to B at a speed of 20 km/hr and returns at a speed of 30 km/hr. The average speed of the car for the whole journey is:
A. 5 km/hr
B. 24 km/hr
C. 25 km/hr
D. 50 km/hr

Answer 1

Hint: The average speed of the car is calculated as the ratio of the total distance covered by the total time taken to cover that distance. As in the options also the unit is given as km/hr thus there is no need to change the unit of speed from km/hr to m/s.
Formula used:
\[{{s}_{avg}}=\dfrac{{{d}_{total}}}{{{t}_{total}}}\]

Complete step-by-step solution:
From given, we have,
The speed of a car travelled from A to B = 20 km/hr
The speed of a car travelled from B to A = 30 km/hr
The average speed equation is given by,
\[{{s}_{avg}}=\dfrac{{{d}_{total}}}{{{t}_{total}}}\]
Where \[{{d}_{total}}\]is the total distance covered and \[{{t}_{total}}\]is the total time taken
Let ‘x’ be the distance covered by a car from A to B.
Then, the time taken by a car to travel from A to B at a speed of 20 km/hr is given as follows:
\[{{t}_{1}}=\dfrac{x}{20}hr\] …… (1)
Similarly, let ‘x’ be the distance covered by a car from B to A.
Then, the time taken by a car to travel from B to A at a speed of 30 km/hr is given as follows:
\[{{t}_{2}}=\dfrac{x}{30}hr\] …… (2)
Therefore, the total time taken by a car for the whole journey is given as follows:
\[t={{t}_{1}}+{{t}_{2}}\] …… (3)
Substitute the equations (1) and (2) in the equation (3) to obtain the expression for the total time taken by a car.
\[t=\dfrac{x}{20}+\dfrac{x}{30}\]
Upon further solving the above equation, we get,
\[\begin{align}
  & t=\dfrac{50x}{600} \\
 & t=\dfrac{5x}{60} \\
 & {{t}_{total}}=\dfrac{x}{12} \\
\end{align}\]
Now compute the total distance covered by a car to travel from A to B and again from B to A.
Therefore, the total distance is given by,
Total distance = Distance covered by a car from A to B + Distance covered by a car from B to A
\[\begin{align}
  & d=x+x \\
 & {{d}_{total}}=2x \\
\end{align}\]
Now compute the average speed of a car for the whole journey.
The average speed is given as follows:
\[\begin{align}
  & {{s}_{avg}}=\dfrac{{{d}_{total}}}{{{t}_{total}}} \\
 & {{s}_{avg}}=\dfrac{2x}{{}^{x}/{}_{12}} \\
 & {{s}_{avg}}=24\,{km}/{hr}\; \\
\end{align}\]
As the average speed of a car for the whole journey is 24 km/hr, thus, option (B) is correct.

Note: The things to be on your finger-tips for further information on solving these types of problems are: The units of the parameters given in the question should be compared to that given in the options. Here students sometimes find the average speed by taking the average of both speeds which makes the solution wrong.