Q. A tram overtakes 2 persons X and Y walking at an average speed of 3 km/hr and 4 km/hr in the same direction and completely passes them in 8 seconds and 9 seconds respectively. What is the length of the tram?

Explanation : 

1. Let the speed of the tram be v km/h and its length be L metres.

2. Speeds of X and Y in km/h:
X: 3 km/h
Y: 4 km/h

3. When overtaking a walker, the tram’s relative speed (in km/h) is (v − walk_speed).
Time to pass completely (in seconds) × relative speed (in km/h) = length (in km), then convert to metres.

4. For X:
• Relative speed = (v − 3) km/h
• Time = 8 s = 8/3600 h
• Distance (tram length L in km) = (v − 3)·(8/3600)

5. For Y:
• Relative speed = (v − 4) km/h
• Time = 9 s = 9/3600 h
• Distance (same L) = (v − 4)·(9/3600)

6. Equate the two expressions for L:
(v − 3)·(8/3600) = (v − 4)·(9/3600)

⇒ 8(v − 3) = 9(v − 4)
⇒ 8v − 24 = 9v − 36
⇒ 36 − 24 = 9v − 8v
⇒ v = 12 km/h

7. Now find L (use X’s data):
L (in km) = (12 − 3)·(8/3600) = 9·(8/3600) = 72/3600 = 1/50 km
L (in metres) = (1/50)·1000 = 20 m

Therefore, the length of the tram is 20 m.