Boats and Streams Exit
Quantitative aptitude

Boats and Streams

Downstream the river helps, upstream it fights. Boat speed is the average of the two; stream speed is half the gap.

Start with this

Rowing with the river's flow, the water carries you: you go faster. Against it, the water pushes back: you go slower.

Boats and streams is relative speed with the river as the second mover. Two formulas cover every question.

Downstream and upstream

Boat speed in still water b, stream speed s. Downstream (with the flow) = b + s. Upstream (against) = b - s.

Going back: b = (down + up) / 2, s = (down - up) / 2.

stream sb + s →← b - sdownstreamupstream
Downstream = boat + stream. Upstream = boat - stream

Downstream and upstream: the rules

Down = b + s, Up = b - s
b = (D + U)/2, s = (D - U)/2
Half the sum, half the difference.

Worked example

A boat goes 24 km downstream in 2 hours and 12 km upstream in 2 hours. Find the boat's speed and the stream's speed.

  1. Down = 12 km/h, Up = 6 km/h.
    Why: Distance / time for each.
  2. b = (12 + 6)/2 = 9. s = (12 - 6)/2 = 3.
  3. Boat 9 km/h, stream 3 km/h.

Answer: Boat 9 km/h, stream 3 km/h

Worked example

A man rows at 5 km/h in still water; the river flows at 1 km/h. It takes him 75 minutes to row to a place and back. How far is the place?

  1. Down 6 km/h, up 4 km/h.
  2. d/6 + d/4 = 5/4 hours.
    Why: 75 minutes = 5/4 h.
  3. (2d + 3d)/12 = 5/4, so 5d = 15.
    Why: Common denominator 12.
  4. d = 3 km.

Answer: 3

Shortcut: Speeds from distances

Use it when: '20 km down in 2 h, 12 km up in 2 h'.

  1. Down 10, up 6.
  2. Boat 8, stream 2.

Speeds from distances: try it

Boat speed?

  1. (10 + 6)/2.

Answer: 8 km/h

Your turn hard

A man rows 48 km and back in 14 h. He can row 4 km downstream in the time he rows 3 km upstream. Stream speed?

  1. Down:up = 4:3 = 4k:3k.
  2. 12/k + 16/k = 14 → k = 2.
  3. Down 8, up 6, stream 1.

Answer: 1 km/h

Your turn medium

A boat takes twice as long upstream as downstream for the same distance. Boat 9 km/h. Stream?

  1. b + s = 2(b - s) → b = 3s.

Answer: 3 km/h

Your turn hard

A boat goes 30 km upstream and 44 km downstream in 10 h, and 40 km up and 55 km down in 13 h. Stream speed?

  1. Up 5, down 11 fits both (6 + 4 = 10, 8 + 5 = 13).
  2. Stream = (11 - 5)/2.

Answer: 3 km/h

Recap

Now practise

4 questions with full solutions.

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