Train Problems – Time and Distance // Type 1: Type 2: Type 3: Type 4

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Train problems are a part of Time and Distance, but the main concept is the length of the train.

Four Rules

1. Train crosses a pole or a person → Distance = Length of the train


2. Train crosses a platform or a bridge → Distance = Length of train + Length of platform/bridge


3. Convert km/h to m/s → Multiply by 5/18 (km/h × 5/18 = m/s)


4. Convert m/s to km/h → Multiply by 18/5 (m/s × 18/5 = km/h)

Remember: km/h → m/s = × 5/18, m/s → km/h = × 18/5

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TYPE 1: Converting Speed (km/h to m/s)

Definition: To convert speed from km/h to m/s, multiply the speed by 5/18.

Q. A train is moving at a speed of 90 km/h. What is its speed in m/s ?

Formula: Speed in m/s = Speed in km/h × 5/18

Solution:

= 90 × 5/18
= 5 × 5
= 25 m/s

Ans: 25 m/s

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TYPE 2: Finding the Length of a Train (Crossing a Pole)

Q. A train moving at 72 km/h crosses a pole in 10 seconds. What is the length of the train ?

Formula: Length of Train = Speed × Time

Where:

• Speed = Speed of the train in m/s


• Time = Time taken to cross the pole in seconds

Solution:

Speed = 72 km/h

Convert km/h into m/s: 72 × 185 ​= 20 m/s

Now,

$$\text{Length}=20\times 10$$ = 200 metres​

Ans: 200 metres

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TYPE 3: Time Taken to Cross a Pole

Definition: Time taken to cross a pole = Length of Train ÷ Speed of Train

Q. A 150-metre-long train is moving at a speed of 54 km/h. How much time will it take to cross a pole ?

Formula: Time = Length of Train / Speed of  Train​

Solution:

Speed = 54 km/h

Convert km/h into m/s: 54 × 5/18​ = 15 m/s

Now,

Time = 150/15​ $$=10\text{ seconds}$$

Ans: 10 seconds

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TYPE 4: Finding the Length of a Platform/Bridge

Definition: Length of Platform = Total Distance − Length of Train

Where: Total Distance = Speed × Time

Q. A 150-metre-long train moving at 90 km/h crosses a bridge in 20 seconds. What is the length of the bridge ?

Formula: $$\text{Length of Bridge }=(\text{Speed}\times \text{Time})-\text{Length of Train}$$

Solution:

Train length = 150 m

Speed = 90 km/h

Convert km/h into m/s: 90 × 5/18​ = 25 m/s

Time = 20 seconds

Total distance: $$25\times 20=500\text{ m}$$

Therefore,

$$\text{Length of Bridge }=500-150$$ = 350 m​

Ans: 350 metres

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