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Speed, Distance, Time & Trains

Quantitative Aptitude · Time-Work & Time-Speed-Distance

Useful for: SSC CGL

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Overview

Distance = speed × time; trains, boats and races are this one relation with the correct distance and relative speed.

Key points

km/h to m/s: multiply by 5/18; m/s to km/h: multiply by 18/5.
Train crossing a pole or person: distance = length of train.
Train crossing a platform or bridge: distance = train length + platform length.
Relative speed: opposite directions add; same direction subtract.
Average speed for equal distances at x and y: 2xy/(x + y).

Explanation

Boats: downstream = boat + stream; upstream = boat − stream; boat = (down + up)/2; stream = (down − up)/2.
When the time is fixed, distance ∝ speed; when distance is fixed, time ∝ 1/speed.
Two trains crossing each other: distance = sum of their lengths.
Late/early problems: difference in time at two speeds gives the distance.

Step by step

Convert units.
Find distance and relative speed.
Divide and check the unit of the answer.

Examples

A 150 m train at 54 km/h (15 m/s) crosses a pole in 150/15 = 10 s and a 250 m platform in 400/15 ≈ 26.67 s.
Equal distances at 40 km/h and 60 km/h: average speed = 2 × 40 × 60/100 = 48 km/h.
Boat 12 km/h in still water, stream 3 km/h: downstream 15 km/h, upstream 9 km/h.

Traps and advanced points

Trap: Taking the simple mean of two speeds as average speed.
Trap: Forgetting to add the platform length.
Trap: Mixing km/h and m/s in one calculation.

Quick revision

× 5/18 to m/s.
Equal distances → 2xy/(x+y).
Opposite add, same subtract.

Practice MCQs

A car covers 240 km in 4 hours. Its speed in m/s is:
1. 16.67 m/s
2. 60 m/s
3. 20 m/s
4. 18 m/s
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Answer: (a) 16.67 m/s. Speed = 240/4 = 60 km/hr.
A train 150 m long crosses a pole in 15 seconds. Its speed is:
1. 30 km/hr
2. 40 km/hr
3. 45 km/hr
4. 36 km/hr
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Answer: (d) 36 km/hr. Pole cross → distance = train length = 150 m.
A train 200 m long moving at 72 km/hr crosses a platform 300 m long in:
1. 25 seconds
2. 20 seconds
3. 30 seconds
4. 22 seconds
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Answer: (a) 25 seconds. Platform cross → distance = 200+300 = 500 m.
A man covers a distance at 4 km/hr and returns at 6 km/hr. His average speed for the whole journey is:
1. 5.2 km/hr
2. 4.8 km/hr
3. 5 km/hr
4. 4.5 km/hr
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Answer: (b) 4.8 km/hr. Same distance dono taraf → average = 2xy/(x+y) = 2×4×6/(4+6) = 48/10 = 4.8 km/hr.
Two trains of lengths 120 m and 80 m run in opposite directions at 42 km/hr and 30 km/hr. Time to cross each other:
1. 15 seconds
2. 10 seconds
3. 12 seconds
4. 8 seconds
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Answer: (b) 10 seconds. Opposite → relative speed = 42+30 = 72 km/hr = 20 m/s.
A boat goes 20 km downstream in 2 hours and returns in 4 hours. The speed of the stream is:
1. 1.5 km/hr
2. 2.5 km/hr
3. 2 km/hr
4. 3 km/hr
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Answer: (b) 2.5 km/hr. Downstream speed = 20/2 = 10; Upstream = 20/4 = 5.
A person walking at 5 km/hr reaches office 6 min late; at 6 km/hr reaches 4 min early. Distance to office:
1. 5 km
2. 4 km
3. 6 km
4. 4.5 km
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Answer: (a) 5 km. Time difference = 6+4 = 10 min = 1/6 hr.
A train travelling at 60 km/hr crosses another train of same length travelling at 40 km/hr in the same direction in 36 seconds. Length of each train:
1. 150 m
2. 100 m
3. 120 m
4. 90 m
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Answer: (b) 100 m. Same direction → relative = 60-40 = 20 km/hr = 50/9 m/s.
If a car's speed is increased by 25%, the time to cover a fixed distance decreases by:
1. 15%
2. 30%
3. 20%
4. 25%
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Answer: (c) 20%. Speed aur time inversely proportional.
A thief runs at 8 km/hr; a policeman 100 m behind chases at 10 km/hr. Time to catch the thief:
1. 5 minutes
2. 3 minutes
3. 2 minutes
4. 4 minutes
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Answer: (b) 3 minutes. Relative speed = 10-8 = 2 km/hr.