**Quantity I:** A train running at a speed of *s* km/h crosses a man moving in the same direction along the railway track at 4 km/h. The man can see the train for 3 minutes. At the moment the train disappears from the man's sight, the distance between the train and the man is 0.8 km. The length of the train is 200 meters. Find the value of *s*.

**Quantity II:** A train crosses a man running in the same direction at 2 m/s in 10 seconds. The same train crosses a tunnel in 54 seconds. If the speed of the train is 72 km/h, find the length of the tunnel.

Compare Quantity I and Quantity II:

Question

**Quantity I:** A train running at a speed of *s* km/h crosses a man moving in the same direction along the railway track at 4 km/h. The man can see the train for 3 minutes. At the moment the train disappears from the man's sight, the distance between the train and the man is 0.8 km. The length of the train is 200 meters. Find the value of *s*.

**Quantity II:** A train crosses a man running in the same direction at 2 m/s in 10 seconds. The same train crosses a tunnel in 54 seconds. If the speed of the train is 72 km/h, find the length of the tunnel.

Compare Quantity I and Quantity II:

Accepted Answer

**Solution:**

**Quantity I:**

1. Let the speed of the train be *s* km/h.
2. The man is moving at 4 km/h in the same direction.
3. The relative speed of the train with respect to the man is $(s - 4)$ km/h.

4. The man can see the train for 3 minutes = $\frac{3}{60} = 0.05$ hours.

5. The train disappears when the distance between the train and the man is 0.8 km.

6. The total distance covered by the train relative to the man during this time includes the length of the train plus the distance 0.8 km:
   $$	ext{Distance} = 0.2 	ext{ km (length of train)} + 0.8 	ext{ km} = 1 	ext{ km}$$

7. Using the formula: Distance = Speed × Time,
   $$1 = (s - 4) 	imes 0.05$$

8. Solving for *s*:
   $$s - 4 = \frac{1}{0.05} = 20$$
   $$s = 24 	ext{ km/h}$$

**Quantity II:**

1. Speed of train = 72 km/h = $\frac{72 	imes 1000}{3600} = 20$ m/s.

2. The man runs at 2 m/s in the same direction.

3. Time taken to cross the man = 10 seconds.

4. Relative speed of train with respect to man = $(20 - 2) = 18$ m/s.

5. Length of train = Speed × Time = $18 	imes 10 = 180$ meters.

6. Time to cross the tunnel = 54 seconds.

7. Total distance covered while crossing the tunnel = Length of train + Length of tunnel.

8. Distance = Speed × Time = $20 	imes 54 = 1080$ meters.

9. Length of tunnel = $1080 - 180 = 900$ meters = 0.9 km.

**Comparison:**

- Quantity I = 24 km/h
- Quantity II = 0.9 km (length of tunnel)

Since Quantity I is in km/h and Quantity II is in km, we need to compare in the same units. However, the question asks to compare Quantity I and Quantity II as given.

Given the context, Quantity I (speed 24 km/h) is less than Quantity II (length 0.9 km) if we consider numerical values directly.

Therefore, **Quantity I < Quantity II**.

**Answer:** (b) Quantity I < Quantity II

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