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Q.

A train covers half of its journey with a speed of $30 m / s$ and another half with a speed of $40 m / s$ . Calculate its average speed for the entire journey?

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a

30.3 m / s

b

30 m / s

c

23 m / s

d

34.3 m / s

answer is D.

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Detailed Solution

A train covers half of its journey with a speed of

30 m / s

and another half with a speed of

40 m / s

. The average speed of the train throughout the journey is

34.3 m / s

.
Let,

s

be the total distance,

t_{1}

and

t_{2}

are durations for covering the first half and second half of the total distance.

\frac{s}{2} = 30 t_{1}

And,

\frac{s}{2} = 40 t_{2}

So total time duration,

t_{1} + t_{2} = s (\frac{1}{60} + \frac{1}{80})

Average velocity

= \frac{s}{t_{1} + t_{2}}

= \frac{240}{7} m / s

= 34.3 m / s

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A train covers half of its journey with a speed of 30 m/s and another half with a speed of 40 m/s. Calculate its average speed for the entire journey?