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Trains Boats And Streams

    • Theory
    • Set 1
    • Set 2
    • Set 3
    • Set 4
    • Set 1
    • Set 2
  1. Aptitude
  3. Quantitative
  5. Trains, Boats and Streams
  7. Theory

Trains, Boats and Streams: Concepts, Formulas, and Clear Examples

Trains: distance = speed × time with train length added to bridge/platform when crossing. Relative speed for opposite/same direction.

Boats: downstream = u+v, upstream = u−v where uuu is boat in still water, vvv stream speed.

Convert km/h and m/s with ×518\times\frac{5}{18}×185​ and ×185\times\frac{18}{5}×518​ before mixing units.

Train crossing pole/platform

Cross object length L

t=train length+Lspeedt = \frac{\text{train length} + L}{\text{speed}}t=speedtrain length+L​

Example — 150 m train at 54 km/h

Speed = 54×518=15 m/s54\times\frac{5}{18}=15\text{ m/s}54×185​=15 m/s. Pole: t=150/15=10 st=150/15=10\text{ s}t=150/15=10 s.

Two trains

Opposite direction

Srel=S1+S2S_{\text{rel}} = S_1 + S_2Srel​=S1​+S2​

Same direction

Srel=∣S1−S2∣S_{\text{rel}} = |S_1 - S_2|Srel​=∣S1​−S2​∣

Boat downstream/upstream

Downstream

Sd=u+vS_d = u + vSd​=u+v

Upstream

Su=u−vS_u = u - vSu​=u−v

Boat speed

u=Sd+Su2, v=Sd−Su2u = \frac{S_d + S_u}{2},\ v = \frac{S_d - S_u}{2}u=2Sd​+Su​​, v=2Sd​−Su​​

Average speed trips

  • Equal distance up/down stream: harmonic mean on times, not speeds.

Unit conversion

km/h to m/s

m/s=km/h×518\text{m/s} = \text{km/h} \times \frac{5}{18}m/s=km/h×185​

Platform vs bridge

  • Include full length to be covered beyond train’s own length.
  • Two trains crossing: sum of lengths over relative speed.

Step-by-step method for exam questions

  1. Convert all speeds to m/s if lengths in meters.
  2. Write total distance (sum lengths if needed).
  3. Pick relative speed for meeting/passing cases.
  4. Time = distance/speed.
  5. For boats, solve u,v from downstream/upstream times if given.
  6. Select option.

Formula cheat sheet

SituationFormulaWhen to use
Train crosses polet=L/St=L/St=L/SDistance = train length
Opposite trainsS1+S2S_1+S_2S1​+S2​Relative speed
Boat still water u(Sd+Su)/2(S_d+S_u)/2(Sd​+Su​)/2From stream speeds
Stream v(Sd−Su)/2(S_d-S_u)/2(Sd​−Su​)/2From stream speeds
km/h→m/s×5/18\times 5/18×5/18With meter lengths

Frequently asked questions

Train on platform person?

Distance often train length only if person is point object.

Same direction overtaking?

Relative speed = difference; distance = sum of lengths.

Round trip river avg speed?

Total distance / total time, not avg of upstream/downstream speeds.

Minutes in time?

Convert to hours or use consistent m/s with seconds.

Practice on this platform

Use 4 practice sets (10 MCQs, detailed solution after each answer) and 2 timed mocks (20 minutes) on this topic to convert formulas into speed and accuracy.

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