**Find the Time Taken by a Train to Cross a Bridge or Tunnel :**

In this section, we will learn how to find the time taken by a train to cross a bridge or tunnel.

Time taken by a train of length l meters to pass a standing object of length b meters is the time taken by the train to cover (l + b) meters.

The relationship between distance, speed and time.

Time = Distance / Speed

Speed = Distance / Time

Distance = Time ⋅ Speed

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 is moving at a speed of 132 km/hr. If the length of the train is 110 meters, how long will it take to cross a railway platform 165 meters long.

**Solution :**

Standing object is railway platform of length 165 meters.

Moving object is train of length 110 meters and running at the speed of 132 km/hr.

Converting the speed from km/hr to m/sec

= 132 ⋅ (5/18)

= 22 ⋅ (5/3)

= (110/3) m/sec

Distance to be covered = 110 + 165

= 275 m

Time = distance / speed

= 275 / (110/3)

= 275 ⋅ (3/110)

= 7.5 seconds

So, the train of length 100 m long is taking 7.5 seconds to cross the railway platform 165 meters long.

**Example 2 : **

How long does a train 110 meters long running at the speed of 72 km/hr take to cross a bridge 132 meters in length ?

**Solution :**

Standing object is bridge of length 132 meters.

Moving object is train of length 110 meters.

Distance to be covered = 132 + 110

= 242 meters

Speed of the train = 72 km/hr

Speed in m/sec = 72 ⋅ (5/18)

= 20 m/sec

Time = Distance / Speed

= 242 / 20

= 12.1 seconds

So, the train of length 132 m is taking 12.1 seconds crosses the bridge of length 110 m.

**Example 3 :**

A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed.

**Solution :**

Let l and x be the length and speed of the train respectively.

The train of length l meters crosses a railway bridge of length 180 m in 20 seconds.

Time = Distance / Speed

20 = (l + 180) / x

x = (l + 180)/20 -----(1)

The train of length l meters crosses a man in 8 seconds.

8 = l / x

x = l / 8 -----(2)

(1) = (2)

(l + 180)/20 = l / 8

8(l + 180) = 20l

20l - 8l = 1440

12l = 1440

l = 1440/12

l = 120

By applying the value of l in (2), we get

x = 120/8

x = 15 m/sec

x = 15 (18/5)

x = 54 km/hr

Hence the length of the train is 120 m and speed is 54 km/hr.

After having gone through the stuff given above, we hope that the students would have understood how to find the time taken by a train to pass a man.

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