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Speed, Distance & Trains

Quantitative Aptitude / DI · Arithmetic Applications

Useful for: Railway RRB, IBPS Banking, CTET, OTET, OSSTET, UGC NET, OSSC RHT — Regular High School Teacher, UPSC NDA/NA

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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 train 880 m long runs at 72 km/h. Time to cross a pole?
1. 44 s
2. 48.4 s
3. 52.8 s
4. 39.6 s
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Answer: (a) 44 s. Convert speed: 72 km/h = 20 m/s.
A train 990 m long runs at 54 km/h. Time to cross a pole?
1. 72.6 s
2. 59.4 s
3. 79.2 s
4. 66 s
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Answer: (d) 66 s. Convert speed: 54 km/h = 15 m/s.
A train 1000 m long runs at 72 km/h. Time to cross a pole?
1. 55 s
2. 50 s
3. 45 s
4. 60 s
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Answer: (b) 50 s. Convert speed: 72 km/h = 20 m/s.
A train 1100 m long runs at 36 km/h. Time to cross a pole?
1. 132 s
2. 99 s
3. 121 s
4. 110 s
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Answer: (d) 110 s. Convert speed: 36 km/h = 10 m/s.
A train 220 m long runs at 36 km/h. Time to cross a pole?
1. 24.2 s
2. 26.4 s
3. 19.8 s
4. 22 s
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Answer: (d) 22 s. Convert speed: 36 km/h = 10 m/s.
A boat moves at 37 km/h in still water and the stream speed is 2 km/h. Its upstream speed is?
1. 39 km/h
2. 35 km/h
3. 33 km/h
4. 37 km/h
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Answer: (b) 35 km/h. Upstream = boat − stream.
A boat moves at 48 km/h in still water and the stream speed is 3 km/h. Its upstream speed is?
1. 43 km/h
2. 49 km/h
3. 45 km/h
4. 47 km/h
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Answer: (c) 45 km/h. Upstream = boat − stream.
A boat moves at 59 km/h in still water and the stream speed is 4 km/h. Its upstream speed is?
1. 55 km/h
2. 59 km/h
3. 53 km/h
4. 57 km/h
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Answer: (a) 55 km/h. Upstream = boat − stream.
A boat moves at 70 km/h in still water and the stream speed is 5 km/h. Its upstream speed is?
1. 63 km/h
2. 69 km/h
3. 65 km/h
4. 67 km/h
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Answer: (c) 65 km/h. Upstream = boat − stream.
A boat moves at 81 km/h in still water and the stream speed is 6 km/h. Its upstream speed is?
1. 79 km/h
2. 75 km/h
3. 77 km/h
4. 73 km/h
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Answer: (b) 75 km/h. Upstream = boat − stream.
A boat moves at 84 km/h in still water and the stream speed is 4 km/h. Its upstream speed is?
1. 80 km/h
2. 84 km/h
3. 78 km/h
4. 82 km/h
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Answer: (a) 80 km/h. Upstream = boat − stream.
A boat moves at 17 km/h in still water and the stream speed is 2 km/h. Its upstream speed is?
1. 19 km/h
2. 15 km/h
3. 13 km/h
4. 17 km/h
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Answer: (b) 15 km/h. Upstream = boat − stream.
A boat moves at 108 km/h in still water and the stream speed is 3 km/h. Its upstream speed is?
1. 103 km/h
2. 107 km/h
3. 105 km/h
4. 109 km/h
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Answer: (c) 105 km/h. Upstream = boat − stream.
A boat moves at 71 km/h in still water and the stream speed is 6 km/h. Its upstream speed is?
1. 67 km/h
2. 69 km/h
3. 63 km/h
4. 65 km/h
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Answer: (d) 65 km/h. Upstream = boat − stream.
A boat moves at 82 km/h in still water and the stream speed is 2 km/h. Its upstream speed is?
1. 84 km/h
2. 82 km/h
3. 78 km/h
4. 80 km/h
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Answer: (d) 80 km/h. Upstream = boat − stream.