Question

A train moving at uniform speed takes 20 seconds to pass a cyclist riding at 11 km/hr but only 9 seconds to pass a
post. Find its length​

Answer 1

Let length of train is is ‘L’ km and speed ‘S’ Km/hr

L/X-11 = 20/3600 = 1/180

L/X = 9/3600 = 1/400

X = 400 L

180 L = X – 11

180L = 400L-11

220L = 11

L = 11/220 = 1/20 KM = 1000/20 =50 meters

Answer 2

Therefore the length of the train is 50 m.

Given:

Time taken by the train to pass the cyclist = t₁ = 20 seconds

Speed of the cyclist = u = 11 kmph = 11 × 5/18 = 55/18 m/s

Time taken by the train to pass the pole = t₂ = 9 seconds

To Find:

The length of the train.

Solution:

The given questions can be answered very easily as shown below.

Let  the length of the train = L

Let the velocity of the train = v

As the time taken by the train to pass the cyclist is more than the time taken by the train to pass the pole, the cyclist and the train are moving in the same direction.

⇒ Speed = distance/time

distance = length of the train.

Case-1: Train passing the cyclist:

As the cyclist moves in the same direction, the relative speed of the train with respect to the cyclist = v - u

So the relative speed of the train with respect to the cyclist is given by,

⇒ ( v-u ) = L/t₁

⇒ ( v-55/18 ) = L/20

⇒ 18v - 55 = 9L/10     (i.)

Case-(ii.): Train passing the pole:

As the pole is stationary, the relative speed of the train with respect to the pole is v ( v - 0 = v )

⇒ v = L/ t₂ ⇒ v = L/9     (ii.)

Substitute v = L/9 in equation-(i.)

⇒ 18v - 55 = 9L/10

⇒ 18( L/9 ) - 55 = 9L/10

⇒ 2L - 9L/10 = 55

⇒ 11L/10 = 55

⇒ L = 5 × 10 = 50 m

Therefore the length of the train is 50 m.

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