Question

Abdul, while driving to school, computes the average speed for his trip to be $20km{{h}^{-1}}$. On his return trip along the same route, there is less traffic and the average speed is $30km{{h}^{-1}}$. What is the average speed of Abdul’s trip?

Answer 1

Hint: The average speed can be given as, ratio of total distance travelled and total time taken to travel that distance, which can be given mathematically as, ${{V}_{avg}}=\dfrac{\text{total distance travelled}}{\text{total time taken}}$, now as the distance remains same in a round trip we will calculate the speed and time by using the relation $\text{distance}=\text{speed }\!\!\times\!\!\text{ time}$and then we will find the average speed of Abdul on the trip.

Formula used: ${{V}_{avg}}=\dfrac{\text{total distance travelled}}{\text{total time taken}}$, $\text{distance}=\text{speed }\!\!\times\!\!\text{ time}$

Complete step-by-step solution -
In question it is given that Abdul, while driving to school, computes the average speed for his trip to be $20km{{h}^{-1}}$. On his return trip along the same route, there is less traffic and the average speed is $30km{{h}^{-1}}$. And we are asked to find the average velocity of Abdul on the trip.
So, let us suppose that the distance of school is $x\ m$, so, the relation between speed, distance and time can be given as,
$\text{distance}=\text{speed }\!\!\times\!\!\text{ time}$ ………………(i)
Now, speed is $20km{{h}^{-1}}$ so, distance for trip 1 can be given as,
$x={{s}_{1}}\times {{t}_{\text{1}}}\ \text{m}$
$x=20\times {{t}_{\text{1}}}\ \text{m}$
Or ${{t}_{1}}=\dfrac{x}{30}\ s$
In the same way for round trip speed is $30km{{h}^{-1}}$ so, the distance for trip 2 can be given as,
$x={{s}_{2}}\times {{t}_{2}}\ \text{m}$
$x=30\times {{t}_{2}}\ \text{m}$
Or ${{t}_{2}}=\dfrac{x}{30}\ s$
Now, the average speed can be defined as ratio of total distance travelled by an object to the total time taken to travel that distance, which can be shown mathematically as,
${{V}_{avg}}=\dfrac{x+x}{\dfrac{x}{20}+\dfrac{x}{30}}$
$\Rightarrow {{V}_{avg}}=\dfrac{2x}{\dfrac{30x+20x}{20\times 30}}$
$\Rightarrow {{V}_{avg}}=\dfrac{2\left( 600 \right)}{50}=2\left( 12 \right)=24\ km{{h}^{-1}}$
Thus, we can say that the average speed of Abdul in trip is $24\ km{{h}^{-1}}$.

Note: Here, the time taken by Abdul for the round trip was not given in the question so we replaced it with speed and distance, but if the time is given then we have to use its value in the formula of average speed. And students must also remember that in a round trip the distance of the starting point and ending point is always the same so we have used $x\ m$ in both the trips.