Train Crossing Time Ratio Same and Opposite Direction

❓ Question

A passenger train of length $60\text{ m}$ travels at speed $80\text{ km/h}$.
Another freight train of length $120\text{ m}$ travels at speed $30\text{ km/h}$.

Find the ratio of time taken by the passenger train to completely cross the freight train:

1. When both move in same direction
2. When both move in opposite directions.

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🖼 Question Image

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✍️ Short Explanation

This problem is based on:

👉 Relative velocity
👉 Train crossing problems
👉 Same vs opposite direction motion.

Main idea:

$$\text{Time}=\frac{\text{Total Length}}{\text{Relative Speed}}$$

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🔷 Step 1 — Total Distance to Cross 💯

To completely cross each other:

$$\text{Total length}=60+120$$
$$=180\text{ m}$$

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🔷 Step 2 — Same Direction Motion

Relative speed:

$$80-30=50\text{ km/h}$$

Convert into m/s:

$$50\times\frac{5}{18} =\frac{250}{18}\text{ m/s}$$

Time taken:

$$t_1=\frac{180}{250/18}$$
$$t_1=\frac{3240}{250}$$
$$t_1=12.96\text{ s}$$

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🔷 Step 3 — Opposite Direction Motion

Relative speed:

$$80+30=110\text{ km/h}$$

Convert into m/s:

$$110\times\frac{5}{18} =\frac{550}{18}\text{ m/s}$$

Time taken:

$$t_2=\frac{180}{550/18}$$
$$t_2=\frac{3240}{550}$$
$$t_2=5.89\text{ s}$$

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🔷 Step 4 — Ratio of Times

$$\frac{t_1}{t_2} = \frac{12.96}{5.89}$$

Using relative speed shortcut:

$$\frac{t_1}{t_2} = \frac{110}{50}$$
$$= \frac{11}{5}$$

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🔷 Step 5 — Final Answer

$$\boxed{\frac{11}{5}}$$

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🔷 Step 6 — JEE Trap Alert 🚨

❌ Train lengths add karna bhool jaana

❌ Same direction mein speeds add kar dena

❌ km/h to m/s conversion miss kar dena

Remember:

$$\text{Same direction} \rightarrow \text{Subtract speeds}$$
$$\text{Opposite direction} \rightarrow \text{Add speeds}$$

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✅ Final Answer

$$\boxed{\frac{11}{5}}$$

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📚 Related Topics

• Relative Motion with Upward Accelerating Frame
• Displacement of Charged Particle in Two B Fields
• Acceleration Velocity Displacement vs Time Graphs