Question

a car taveles at a speed of 20kmper houe and returs back wiha speed of 30kmperhour find the average speed of the ehole journey

Answer 1

Answer:

24 km/h

Explanation:

Let us assume that the body starts from point P and covers certain distance and comes to point Q. Suppose the distance from P to Q as x km.

Now, according to the question, it has been stated that,

• A car travels at a speed of 20 km/h.
• Then, it returns back with speed of 30 km/h.

We've been asked to calculate the average speed of the whole journey.

Here, in order to calculate the average speed of the whole journey, firstly we need to calculate the total distance and total time taken. Here,

$\underline{\large \sf {\maltese \; \; \; Total \: distance \: travelled : \; \; \; }}$

It goes from P to Q and then again comes to P. So,

$\longrightarrow \sf{\quad {Distance_{(Total)} = PQ + QP}}$

$\longrightarrow \sf{\quad {Distance_{(Total)} = (x + x) \; km}}$

$\longrightarrow \quad \boxed{\sf {Distance_{(Total)} = 2x\; km}}$

$\underline{\large \sf {\maltese \; \; \; Total \: time \: taken : \; \; \; }}$

Here, we aren't given that how much time is taken by the car to travel from P to Q and vice-versa. We are only provided with magnitude of speed.

★ Time = Distance/Speed

Thus,

$\longrightarrow \sf{\quad { Time_{(Total)} = Time_{(PQ)} + Time_{(QP)}}}$

$\longrightarrow \sf{\quad {Time_{(Total)} = \dfrac{Distance_{(PQ)}}{Speed_{(PQ)}} + \dfrac{Distance_{(QP)}}{Speed_{(QP)}} }}$

• Speed from P to Q is 20 km/h.
• Speed from Q to P is 30 km/h.

$\longrightarrow \sf{\quad {Time_{(Total)} = \Bigg \{ \dfrac{x}{20} + \dfrac{x}{30} \Bigg \} \; h}}$

$\longrightarrow \sf{\quad {Time_{(Total)} = \Bigg \{ \dfrac{3x + 2x}{60} \Bigg \} \; h}}$

$\longrightarrow \sf{\quad {Time_{(Total)} = \Bigg \{ \dfrac{5x}{60} \Bigg \} \; h}}$

$\longrightarrow \quad \boxed{\sf {Time_{(Total)} = \dfrac{x}{12} \; h}}$

Now, as we know that,

$\bigstar \quad\underline{\boxed { \pmb{\frak{Speed}}_{\pmb{\frak{(Avg)}}} = \dfrac{\pmb{\frak{Distance}}_{\pmb{\frak{(Total)}}} }{\pmb{\frak{Time}}_{\pmb{\frak{(Total)}}} } }}$

Substitute the values.

$\longrightarrow \sf{\quad { Speed_{(Avg)} = \Bigg \{ 2x \div \dfrac{x}{12} \Bigg \} \; km \: h^{-1} }}$

$\longrightarrow \sf{\quad { Speed_{(Avg)} = \Bigg \{ 2x \times \dfrac{12}{x} \Bigg \} \; km \: h^{-1} }}$

$\longrightarrow \sf{\quad { Speed_{(Avg)} = \Bigg \{ 2 \times 12 \Bigg \} \; km \: h^{-1} }}$

$\longrightarrow \quad \underline{\boxed {\pmb{\frak{Speed}}_{\pmb{\frak{(Avg)}}} = \pmb{\frak{24 \; km }}\: \pmb{\frak{h}}^{\pmb{\frak{-1}}} }}$

Therefore, average speed is 24 km/h.