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Last updated date: 01st Dec 2023
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MVSAT Dec 2023

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.

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Hint: 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.