Speed, Distance, Trains & Boats

Speed = Distance / Time. Pay strict attention to unit conversions: multiplying km/h by 5/18 converts to m/s, while multiplying m/s by 18/5 converts to km/h.

Exam Frequency: 2 to 4 questions in IT placement and PSU tests

Essential Formulas & Shortcut Rules

1 km/h = 5/18 m/s

Standard unit conversion factor.

Average Speed (equal distance) = (2 × S₁ × S₂) / (S₁ + S₂)

Harmonic mean of two speeds.

Relative Speed (Opposite Direction) = S₁ + S₂

Speeds add when approaching each other.

Relative Speed (Same Direction) = |S₁ - S₂|

Speeds subtract when moving in same direction.

Downstream Speed = u + v; Upstream Speed = u - v

u = boat speed in still water, v = stream speed.

Worked Step-by-Step Examples

Example 1: A train 180 meters long is traveling at a speed of 72 km/h. How many seconds will it take to completely pass a railway platform of length 220 meters?

Step-by-Step Mathematical Derivation:

•Convert train speed from km/h to m/s: 72 × (5/18) = 4 × 5 = 20 m/s.

•Total distance to cover = Length of Train + Length of Platform = 180 + 220 = 400 meters.

•Time taken = Distance / Speed = 400 / 20 = 20 seconds.

Answer: 20 seconds

💡 Speed Shortcut: Always convert units into consistent SI (meters and seconds) before attempting arithmetic.

Common Exam Traps to Avoid

✕Calculating average speed as arithmetic mean (S₁ + S₂)/2 when distances are equal (arithmetic mean only applies if times are equal).
✕Forgetting to add the length of the platform to the length of the train.

Interactive Practice Drill (2 Questions)

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Speed, Distance, Trains & Boats Practice Drill

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1Speed, Distance, Trains & Boats

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A motorist travels from City A to City B at an average speed of 60 km/h and returns along the same route at 40 km/h. What is the average speed for the entire round trip?

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