Question

Akhil drove his car with a speed of 20km/h while going to his college when he returned to his home along the same route the speed of the car was 30km/h. Calculate the average speed of the car during the entire journey.

Answer 1

To answer this question, we first need to understand what speed and average speed is. The rate at which an object travels over a given distance is known as speed. The average speed of an object in a given time period is the object's distance travelled divided by the interval's length; the instantaneous speed is the average speed's limit as the interval's duration reaches nil.

Complete step by step answer:
As given in the question speed of the car when going to college = 20Km/h,
And speed of the car while returning back to home = 30Km/h.
Let the distance from Akhil’s home to college be x Km, so total distance travelled by Akhil is 2x Km.
Formula of speed

$$ Speed = $\dfrac{D}{T}$(where D is the distance travelled and T is the time taken) Let the time taken by Akhil while going to college be ${t_1}$ Substituting the value in formula $20\dfrac{{Km}}{h} = \dfrac{{xKm}}{{{t_1}}}$ Getting the value of ${t_1}$ ${t_1} = \dfrac{x}{{20}}h$ Similarly, assuming the time taken by Akhil while coming back to home be ${t_2}$ Substituting the value in formula $30\dfrac{{Km}}{h} = \dfrac{{xKm}}{{{t_2}}}$ Getting the value of ${t_2}$ ${t_2} = \dfrac{x}{{30}}h$ Total time taken in complete trip = ${t_1} + {t_2}$ i.e. TT = $(\dfrac{x}{{20}} + \dfrac{x}{{30}})h$ Taking LCM TT = $\dfrac{x}{{12}}h$ As discussed above total distance i.e. (TD) = 2xKm/h. As we know that average speed = $\dfrac{{TD}}{{TT}}$ (where TT is the total time and TD is the total distance travelled) Substituting values Average speed = $\dfrac{{2x}}{{x/12}}$(total distance is 2x whereas total time is x/12) So average speed = $2 \times 12 = 24Km/h$ So the final answer is 24Km/h. **Note:** The total distance travelled divided by the time taken equals average speed, while average velocity equals displacement divided by time taken equals average velocity. The average speed is also a scalar quantity since speed is a scalar quantity, while velocity is a vector quantity.