Question

A man covers a certain distance by car driving at 70 km/hr and he returns to the starting point riding on a scooter at 55 km/hr. Find his average speed for the whole journey.
A. 62.5 km/hr
B. 62.8 km/hr
C. 63.6 km/hr
D. 64.6 km/hr

Answer 1

Hint: Here, we will find the time taken for one side journey and the time taken in return journey; and calculate the total time by adding these two.
And find the average speed using formula $\text{Average speed = }{\displaystyle \frac{\text{Total distance travelled}}{\text{Total time taken}}}$.

Complete step by step answer:
Let the distance covered by man by driving a car is d km.
Given, the speed of a car is 70 km/hr.
Let t1 be the time taken to cover a distance d km at a speed of 70 km/h, $$t_1={\displaystyle \frac{d}{70}}$$ hr
As $$\text{Time = }{\displaystyle \frac{\text{Distance}}{\text{Speed}}}$$
Also given that the man covered the same distance in the return journey.
 The distance covered by man in return journey is d km.
Given, the speed of the car in the return journey is 55 km/h.
Let t2 be the time take to cover a distance d km at a speed of 55 km/h, $$t_2={\displaystyle \frac{d}{55}}$$ hr
Total time taken for the whole journey, $$T=t_1+t_2=\left({\displaystyle \frac{d}{70}}+{\displaystyle \frac{d}{55}}\right)$$hr
$T={\displaystyle \frac{d}{5}}\left({\displaystyle \frac{1}{14}}+{\displaystyle \frac{1}{11}}\right)$ hr
On simplifying, we have
$T={\displaystyle \frac{d}{5}}\left({\displaystyle \frac{11+14}{14\times 11}}\right)$ hr
$T={\displaystyle \frac{d}{5}}\left({\displaystyle \frac{25}{154}}\right)={\displaystyle \frac{5d}{154}}$hr
Total distance travelled in the whole journey = $d+d=2d$km
We have, total distance = 2d km and total time taken $T={\displaystyle \frac{5d}{154}}$
Average speed for the whole journey, $S={\displaystyle \frac{\text{Total distance}}{\text{Total time}}}$
$S={\displaystyle \frac{2d}{T}}$
On putting values of 2d and T in $\left(S={\displaystyle \frac{2d}{T}}\right)$
$S={\displaystyle \frac{2d}{{\displaystyle \frac{5d}{154}}}}$
$S={\displaystyle \frac{2\times 154}{5}}={\displaystyle \frac{308}{5}}=61.6$ km/hr

Therefore, the average speed for the whole journey is 61.6 km/hr.
None of the given options is correct.

Note:
In this type of question always calculate time taken for different speeds and add them to get total time. Always keep in mind while solving these types of questions, $$\text{Average speed}\ne {\displaystyle \frac{\text{Sum of speeds}}{\text{2}}}.$$
Alternatively, we can use direct formula of average speed, i.e.$S_{av}={\displaystyle \frac{2S_1{S}_2}{S_1+S_2}}$, where S1 and S2 are the two different speeds for covering same distance.