# 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

Verified

279.6k+ views

**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.

Recently Updated Pages

Basicity of sulphurous acid and sulphuric acid are

Define absolute refractive index of a medium

Which of the following would not be a valid reason class 11 biology CBSE

Why should electric field lines never cross each other class 12 physics CBSE

An electrostatic field line is a continuous curve That class 12 physics CBSE

What is meant by monosporic development of female class 11 biology CBSE

Trending doubts

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which one of the following places is unlikely to be class 8 physics CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

What is the past tense of read class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Elucidate the structure of fructose class 12 chemistry CBSE

What is pollution? How many types of pollution? Define it