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 ${\text{Average speed = }}\dfrac{{{\text{Total distance travelled}}}}{{{\text{Total time taken}}}}$.

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, \[{t_1} = \dfrac{d}{{70}}\] hr
As \[{\text{Time = }}\dfrac{{{\text{Distance}}}}{{{\text{Speed}}}}\]
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, \[{t_2} = \dfrac{d}{{55}}\] hr
Total time taken for the whole journey, \[T{\text{ }} = {\text{ }}{t_1} + {\text{ }}{t_2} = \left( {\dfrac{d}{{70}} + \dfrac{d}{{55}}} \right)\]hr
$T = \dfrac{d}{5}\left( {\dfrac{1}{{14}} + \dfrac{1}{{11}}} \right)$ hr
On simplifying, we have
$T = \dfrac{d}{5}\left( {\dfrac{{11 + 14}}{{14 \times 11}}} \right)$ hr
$T = \dfrac{d}{5}\left( {\dfrac{{25}}{{154}}} \right) = \dfrac{{5d}}{{154}}$hr
Total distance travelled in the whole journey = $d + d = 2d$km
We have, total distance = 2d km and total time taken $T = \dfrac{{5d}}{{154}}$
Average speed for the whole journey, $S = \dfrac{{{\text{Total distance}}}}{{{\text{Total time}}}}$
$S = \dfrac{{2d}}{T}$
On putting values of 2d and T in $\left( {S = \dfrac{{2d}}{T}} \right)$
$S = \dfrac{{2d}}{{\dfrac{{5d}}{{154}}}}$
$S = \dfrac{{2 \times 154}}{5} = \dfrac{{308}}{5} = 61.6$ 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, \[{\text{Average speed}} \ne \dfrac{{{\text{Sum of speeds}}}}{{\text{2}}}.\]
Alternatively, we can use direct formula of average speed, i.e.${S_{av}} = \dfrac{{2{S_1}{S_2}}}{{{S_1} + {S_2}}}$, where S1 and S2 are the two different speeds for covering same distance.