Trains, Relative Speed and Boats & Streams

Relative speed

• Objects moving in opposite directions: relative speed = a + b.
• Objects moving in the same direction: relative speed = a − b.

Train problems

Distance to cover = length of train + length of the object crossed.

• Crossing a pole / man / signal: distance = length of train.
• Crossing a platform / bridge / another train: distance = sum of both lengths.

Example: A 150 m train at 54 km/h (15 m/s) crosses a 300 m platform in (150 + 300)/15 = 30 s.

Boats and streams

Let boat speed in still water = b and stream speed = s.

• Downstream speed D = b + s; upstream speed U = b − s.
• b = (D + U)/2, s = (D − U)/2.

Example: D = 16 km/h, U = 10 km/h → b = 13 km/h, s = 3 km/h.

Exam tips (RRB NTPC)

1. Always convert km/h to m/s when lengths are in metres.
2. Two trains crossing each other: add lengths, use relative speed.

Analogy

Relative speed is like walking on an airport travelator. Walk with the belt and your speeds add up; walk against it and they subtract. A boat going downstream is you walking with the belt; going upstream is walking against it — and the belt's own speed is the stream.