**Problems on Finding the Length of Train :**

In this section, we will learn how to find the length of the train.

Time taken by a train of length l meters to pass a pole or standing man or signal post is equal to the time taken by the train to cover l meters.

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.

Distance covered by both the trains = l + b

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

Relative Speed = (u - v) m / s

Distance covered = Sum of length of two trains

Time = Sum of length of two trains/Relative speed

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

Relative speed = (u + v) m/s

then the time taken by the faster train to cross the slower train is

= Sum of length of two trains/Relative 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 :**

It took a train 50 seconds to pass a tunnel that was 1000 m long. It took the same train, traveling at the same speed, 75 seconds to pass a bridge that was 1625 m long. How long was the train ? At what speed was it travelling ?

**Solution :**

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

Distance covered by the train when it crosses the tunnel of length 1000 m = l + 1000

Time taken = Distance / Speed

50 = (l + 1000) / x

x = (l + 1000) / 50 ------(1)

Distance covered by the train when it crosses the bridge of length (l + 1625)

75 = (l + 1625) / x

x = (l + 1625) / 75 ------(2)

(1) = (2)

(l + 1000) / 50 = (l + 1625) / 75

(l + 1000) / 2 = (l + 1625) / 3

3(l + 1000) = 2(l + 1625)

3l + 3000 = 2l + 3250

3l - 2l = 3250 - 3000

l = 250 m

By applying the value of l in (1)

x = (250 + 1000) / 50

x = 25 m/sec

To convert the speed from m/sec to km/hr, we get

x = 25⋅(18/5)

x = 90 km/hr

Hence the length of the train is 250 m, speed of the train is 50 km/hr.

**Example 2 :**

Two trains travelled towards each other on different tracks. Train A traveled at a speed of 54 km/hr and Train B travelled at 72 km/hr. A commuter aboard Train A recorded that Train B took 8 seconds to pass his window seat completely. How long was Train B ?

**Solution :**

Speed of Train A = 54 km/hr

Speed of Train B = 72 km/hr

Converting the speed from km/hr to m/sec

Speed of train A = 54 ⋅ (5/18) = 15 m/sec

Speed of train B = 72 ⋅ (5/18) = 20 m/sec

Relative speed = 15 + 20

= 35 m/sec

Train B is taking 8 seconds to cross the window seat of train A.

Time = Distance covered by Train B / 35

Distance covered by train B = Length of train B

= 35 ⋅ 8

= 280 m

After having gone through the stuff given above, we hope that the students would have understood problems on finding the length of train

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