A train travelling at $100 ext{ km/h}$ overtakes a motorbike travelling at $64 ext{ km/h}$ in $40$ seconds. What is the length of the train in meters?

Question

A train travelling at $100 	ext{ km/h}$ overtakes a motorbike travelling at $64 	ext{ km/h}$ in $40$ seconds. What is the length of the train in meters?

Accepted Answer

**Solution:**

1. Let the length of the train be *x* meters.

2. The train overtakes the motorbike in 40 seconds. The relative speed between the train and the motorbike is the difference of their speeds.

3. Convert speeds from km/h to m/s:
   - Train speed = $100 	imes \frac{5}{18} = \frac{500}{18} \approx 27.78 	ext{ m/s}$
   - Motorbike speed = $64 	imes \frac{5}{18} = \frac{320}{18} \approx 17.78 	ext{ m/s}$

4. Relative speed = $27.78 - 17.78 = 10 	ext{ m/s}$

5. Time taken to overtake = 40 seconds, so the length of the train is:
   $$x = 	ext{relative speed} 	imes 	ext{time} = 10 	imes 40 = 400 	ext{ meters}$$

**Answer:** $400 	ext{ m}$

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