Question

A car travels 100 km at a speed of 60 km/h and returns with a speed of 40 km/h. Calculate the speed for the whole journey.
A. $48\dfrac{m}{s}$
B. $480\dfrac{{km}}{{hr}}$
C. $48\dfrac{{km}}{{hr}}$
D. $48\dfrac{m}{{hr}}$

Answer 1

Hint:The speed for the whole journey refers to the term average speed. The average speed is the ratio of the total distance travelled and the total time taken for the distance to be travelled. This definition must be applied to calculate the average speed.

Complete step-by-step solution:
The speed is defined as the ratio of the distance travelled per unit time.
$s = \dfrac{d}{t}$
The term average speed gives us a sense of the rate at which the journey is covered. It represents the arithmetic mean of all the values of speed that the body travels over a distance.
If a body covers ${d_1}$ distance in time ${t_1}$ , ${d_2}$ distance in time ${t_2}$ and so on, the average speed is given by the expression,
$S = \dfrac{{{d_1} + {d_2} + \cdot \cdot \cdot }}{{{t_1} + {t_2} + \cdot \cdot }}$
Here, the car travels a total distance of 100km. This total distance includes the distance travelled in the forward journey and the distance travelled in the reverse journey.
The total distance travelled by the car in each trip, $d = 100km$
If the forward journey takes place with the speed of 60 km/hr, the time taken for the journey is given by –
${t_1} = \dfrac{{100}}{{60}} = \dfrac{5}{3}hr$
Similarly, if the reverse journey takes place with the speed of 40 km/hr, the time taken for the journey is given by –
${t_2} = \dfrac{{100}}{{40}} = \dfrac{5}{2}hr$
Calculating the average speed for the journey, we have –
$S = \dfrac{D}{{{t_1} + {t_2}}}$
Here, D is the total distance travelled, which is the sum of forward and return journey. Hence,
$D = 100 + 100 = 200km$
Substituting,
$S = \dfrac{{200}}{{\dfrac{5}{3} + \dfrac{5}{2}}}$
$ \Rightarrow S = \dfrac{{200}}{{25}} \times 6$
$ \Rightarrow S = 8 \times 6$
$\therefore S = 48km - h{r^{ - 1}}$
Therefore, the average speed for the whole journey is 48 km/hr.

Hence, the correct option is Option C.

Note:Though the average speed gives us an indication about how fast the body is moving, the actual speed at every instant may not be uniform. Hence, there is another type of speed known as instantaneous speed, which is used to determine the speed of the body at every instance of the journey.