Question

A car travels between two cities in three parts of equal distances witj speed 30 km/hr, 45 km/hr and 90km/hr respectively. What is average speed of the car?​

Answer 1

Answer:

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Answer 2

Answer:

45 km/h

Explanation:

As per the provided information in the given question, we have :

• A car travels between two cities in three parts of equal distances with speed 30 km/hr, 45 km/hr and 90km/hr respectively.

We are asked to calculate the average speed.

In order to calculate the average speed, firstly we need to calculate the total distance travelled and total time taken.

Let the the distance covered in three parts x km each. Thus,

$\longrightarrow\tt{ Total \; distance = S_1 + S_2 + S_3 } \\ \\\longrightarrow \tt{ Total \; distance = (x + x + x) \;km } \\ \\\longrightarrow\underline{ \tt{ Total \; distance = 3x \; km }}$

Now, we have to find the total time taken. Total time taken will be the sum of the time taken by the car in all the three part.

In the first part :

• $\tt {S_1 = x \; km}$
• $\tt {V_1 = 30 \; km \;h^{-1}}$

In the second part :

• $\tt {S_2 = x \; km}$
• $\tt {V_2 = 45 \; km \;h^{-1}}$

In the third part :

• $\tt {S_3 = x \; km}$
• $\tt {V_3 = 90 \; km \;h^{-1}}$

Now, as it known to us that, time = distance ÷ speed or t = s/t, so

$\longrightarrow \tt { T_{(Total)} = T_1 + T_2 + T_3 }\\ \\ \longrightarrow \tt { T_{(Total)} = \dfrac{S_1}{V_1} + \dfrac{S_2}{V_2} + \dfrac{S_3}{V_3} } \\ \\ \longrightarrow \tt { T_{(Total)} = \Bigg ( \dfrac{x}{30} + \dfrac{x}{45} + \dfrac{x}{90} \Bigg ) \; h } \\ \\ \longrightarrow \tt { T_{(Total)} = \Bigg ( \dfrac{3x + 2x + x}{90} \Bigg ) \; h } \\ \\ \longrightarrow \tt { T_{(Total)} = \Bigg ( \dfrac{6x}{90} \Bigg ) \; h } \\ \\ \longrightarrow \underline{ \tt { T_{(Total)} = \dfrac{x}{15} \; h } }$

Now, let's calculate average speed. Average speed is given by,

$\longrightarrow \boxed{\tt {Speed_{(Avg)} = \dfrac{Distance_{(Total)}}{Time_{(Total)}} }} \\ \\ \longrightarrow\tt {Speed_{(Avg)} = \Bigg ( 3x \div \dfrac{x}{15} \Bigg ) \; km \;h^{-1}} \\ \\ \longrightarrow\tt {Speed_{(Avg)} = \Bigg ( 3x \times \dfrac{15}{x} \Bigg ) \; km \;h^{-1}} \\ \\ \longrightarrow\tt {Speed_{(Avg)} = \Bigg ( 3 \times 15 \Bigg ) \; km \;h^{-1}} \\ \\ \longrightarrow\underline{\boxed{\tt {Speed_{(Avg)} = 45 \; km \;h^{-1}}}} \; \red{\bigstar}$

∴ The average speed is 45 km/h.