**Train Passes a Moving Object in the Same Direction :**

If two trains or two bodies are moving in the same direction at u m/s and v m/s, then their

R elative Speed = (u - v) m / s

Distance covered = Sum of length of two trains

Time = Distance / Speed

Time = Sum of length of two trains / (u - v)

To convert minutes into hour, we should divide the given minutes by 60.

- If we want to convert the speed from km/hr to m/sec, we should multiply the speed by 5/18.
- If we want to convert the speed from m/sec to km/hr, we should multiply the speed by 18/5.

**Example 1 :**

A train 150 m long is running with a speed of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going ?

**Solution :**

The train and a man are travelling in the same direction.

So,

Relative speed = Speed of the train - Speed of the man

= 68 - 8

= 60 km/hr

Converting the speed from km/hr to m/sec

= 60 ⋅ (5/18)

= 50/3

Since the train crosses the man, the distance covered by the train is 150 m (the length of the train).

Time = 150 / (50/3)

= 150 ⋅ (3/50)

= 9 seconds

**Example 2 :**

Two trains 100 meters and 120 meters long are running in the same direction with speeds of 72 km/hr and 54 km/hr. In how much time will the first train cross the second ?

**Solution :**

Since both are moving objects and the total distance covered

= 100 + 120

= 220 meters

Relative speed = 72 - 54

= 18

Relative speed in m/sec = 18 ⋅ (5/18)

= 5 m/sec

Time = Distance / Speed

= 220 / 5

= 44 seconds

Hence the first train is taking 44 seconds to cross the second train.

**Example 3 :**

A train running at 54 kmph takes 20 seconds to pass a platform. Next it takes 12 seconds to pass a man walking at 6 kmph in the same direction in which the train is going. Find the length of the train and length of the platform.

**Solution :**

Let x and y be the length of the train and length of platform.

Distance covered by the train while crossing the platform

= x + y

Time taken by the train to cross the platform = 20 sec

Speed of the train and = 54 km/hr

54 km/hr = 54 ⋅ (5/18)

= 15 m/sec

Time taken by the train to cross the platform is

Time = Distance / Speed

20 = (x + y) / 15 -----(1)

Time taken by the train to cross the platform = 12 sec

Speed of the man = 6 km/hr

Relative speed = 54 - 6

= 48 kmph

48 km/hr = 48 ⋅ (5/18)

= (40/3) m/sec

Time taken by the train to cross a man is

Time = Distance / Speed

12 = x / (40/3)

x = 160

By applying the value of x in (1), we get

20 = (160 + y) / 15

y = 300 - 160

y = 140 m

Hence the length of the train and the length of the platform are 160 m and 140 m respectively.

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