Question

A train travels a distance at a speed of 40 km/h and returns at the speed of 60 km/h.
What is the average speed of the train?

(i)
12 km/h

(ii)
24 km/h

(iii)
16 km/h

(iv)
48 km/h


Pls answer asap…

Answer 1

Answer:

Option IV ( 48 km/h )

Explanation:

Let us suppose the body goes from P to Q and then returns back and assume the distance from P to Q as x km.

According to the question,

• A train travels a distance at a speed of 40 km/h and returns at the speed of 60 km/h.

We have to find the average speed. In order to find the average speed, we need to calculate the total distance and total time taken first.

We have assumed the distance from P to Q x km. As it returns back, so

$\longrightarrow\tt{ Total \; distance = PQ + QP}$

$\longrightarrow\tt{ Total \; distance = (x + x) \; km}$

$\longrightarrow \boxed{\tt{ Total \; distance = 2x \; km}}$

Now, let's find out total time taken.

$\longrightarrow\tt{ Total \; time = t_1 + t_2}$

• $\tt t_1$ is time taken to cover the distance from P to Q.
• $\tt t_2$ is time taken to cover the distance from Q to P.

[ Time = Distance ÷ Speed ]

$\longrightarrow\tt{ Total \; time = \dfrac{s_1}{v_1} + \dfrac{s_2}{v_2} }$

$\longrightarrow\tt{ Total \; time =\Bigg ( \dfrac{x}{40} + \dfrac{x}{60}\Bigg ) \; h}$

$\longrightarrow\tt{ Total \; time =\Bigg ( \dfrac{3x + 2x}{120}\Bigg ) \; h}$

$\longrightarrow \boxed{\tt{ Total \; time =\dfrac{5x}{120} \; h }}$

Now, as we know that,

$\longrightarrow \underline{\boxed{\tt { Speed_{(Avg)} = \dfrac{Total \; distance}{Total \;time} }}}$

Substitute the values.

$\longrightarrow\tt{ Speed_{(Avg)} = \Bigg (2x \div \dfrac{5x}{120} \Bigg ) \; kmh^{-1}}$

$\longrightarrow\tt{ Speed_{(Avg)} = \Bigg (2x \times \dfrac{120}{5x} \Bigg ) \; kmh^{-1}}$

$\longrightarrow\tt{ Speed_{(Avg)} = \Bigg ( \dfrac{240x}{5x} \Bigg ) \; kmh^{-1}}$

$\longrightarrow \boxed{\tt{ Speed_{(Avg)} = 48 \; kmh^{-1}}} \; \bigstar$

Therefore, the average speed is 48 km/h.