Train Problems – Time and Distance // Type 10: Type 11: Type12

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TYPE 10: Pole and Platform – Mixed Problem

Definition: When a train crosses a pole and a platform, the extra time taken to cross the platform helps us find the train's speed.

Q. A train crosses a pole in 10 seconds and a 200 m long platform in 20 seconds. Find the length of the train.

Formula: Train Length = Speed × Time taken to cross the pole

Solution:

Pole-crossing time = 10 s
Platform-crossing time = 20 s

Extra time: $$20-10=10\text{ s}$$

In these extra 10 seconds, the train covers the 200 m platform.

So,

    Speed = 200/10 ​= 20 m/s

Now,

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

Ans: 200 metres

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TYPE 11: Crossing Two Bridges

Definition: When a train crosses a bridge/platform: $$\text{Total Distance }=\text{Train Length }+\text{Bridge Length}$$

Since the train's speed is the same in both cases: L + 500​/100 = L+250/60​

Q. A train crosses two bridges of lengths 500 m and 250 m in 100 seconds and 60 seconds, respectively. Find the length of the train.

Solution

Let the length of the train = L metres.

                                        L+500/100 ​=L+250/ 60​

Cross-multiply:

$$60(L+500)=100(L+250)$$

$$60L+30000=100L+25000$$

$$30000-25000=100L-60L$$

$$5000=40L$$

L = 5000/40​

L = 125 m​

Ans: 125 metres

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TYPE 12: Time of Meeting

Definition: When two trains start from opposite directions and move towards each other, the time taken for them to meet is called the Time of Meeting.

For opposite directions, relative speed = sum of the speeds.

Formula:

Time of Meeting = Distance Between Them / Speed₁ ​+ Speed₂​​

Q. Train A leaves Delhi at 8:00 AM at 60 km/h, and Train B leaves Meerut at 8:00 AM at 40 km/h. The distance between Delhi and Meerut is 200 km. When will they meet ?

Solution:

Speed of Train A = 60 km/h
Speed of Train B = 40 km/h

Relative speed: $$60+40=100\text{ km/h}$$

Time of meeting: 200​/100 = 2 hours

Both trains start at 8:00 AM.

                        8:00 AM + 2 hours = 10:00 AM​

Ans: 10:00 AM

Trick:
Opposite direction → Add speeds

Meeting Time = Distance / Sum of Speeds​​