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Boats and Streams (Upstream / Downstream)

Introduction

Problems on Boats and Streams test how currents (or flow of water) affect the effective speed of a boat. The direction of flow changes the relative speed - helping or opposing the motion.

This pattern is important because many aptitude questions involve upstream (against the current) and downstream (with the current) motion, and mastering this concept makes complex distance-speed relations easy to handle.

Pattern: Boats and Streams (Upstream / Downstream)

Pattern

Key concept: The stream’s current either assists or resists the boat’s motion.

  • Downstream (with current): Effective speed = (Boat speed + Stream speed)
  • Upstream (against current): Effective speed = (Boat speed - Stream speed)
  • Still water: When current = 0, boat speed = its own speed in still water.
  • Average relation:
    • Speed in still water = (Downstream + Upstream) ÷ 2
    • Speed of current = (Downstream - Upstream) ÷ 2

Step-by-Step Example

Question

A boat goes 24 km downstream in 3 hours and returns the same distance upstream in 4 hours. Find the speed of the boat in still water and the speed of the stream.

Solution

  1. Step 1: Find downstream and upstream speeds

    Downstream speed = 24 ÷ 3 = 8 km/h
    Upstream speed = 24 ÷ 4 = 6 km/h

  2. Step 2: Apply formula for still water and current

    Speed in still water = (8 + 6) ÷ 2 = 7 km/h
    Speed of current = (8 - 6) ÷ 2 = 1 km/h

  3. Final Answer:

    Boat in still water = 7 km/h, Current speed = 1 km/h

  4. Quick Check:

    Downstream = 7 + 1 = 8 km/h, Upstream = 7 - 1 = 6 km/h ✅

Quick Variations

1. Finding speed in still water or speed of stream given downstream & upstream.

2. Finding time or distance when traveling both ways.

3. Relative speed concept used when man or object moves on moving water.

4. Questions where current speed is given as fraction of boat’s speed (e.g., one-third or one-fifth).

5. Problems with units conversion (m/s ↔ km/h).

Trick to Always Use

  • Step 1: Write Downstream and Upstream formulas clearly.
  • Step 2: Use (D + U)/2 for boat speed, (D - U)/2 for stream speed.
  • Step 3: Always ensure units are consistent (km/h or m/s).
  • Step 4: Verify using reverse calculation (add/subtract stream speed to get D, U).

Summary

Summary

  • Downstream = Boat + Stream
  • Upstream = Boat - Stream
  • Boat speed = (Downstream + Upstream) ÷ 2
  • Stream speed = (Downstream - Upstream) ÷ 2
  • Convert units when necessary and use cross-verification for accuracy.

Practice

(1/5)
1. A boat goes 16 km downstream in 2 hours and returns the same distance upstream in 4 hours. Find the speed of the boat in still water.
easy
A. 6 km/h
B. 7 km/h
C. 8 km/h
D. 9 km/h

Solution

  1. Step 1: Compute downstream & upstream speeds

    Downstream = 16 ÷ 2 = 8 km/h; Upstream = 16 ÷ 4 = 4 km/h.

  2. Step 2: Use formula for still water

    Boat speed = (Downstream + Upstream) ÷ 2 = (8 + 4) ÷ 2 = 6 km/h.

  3. Final Answer:

    Boat speed in still water = 6 km/h → Option A.

  4. Quick Check:

    Downstream = 6 + 2 = 8; Upstream = 6 - 2 = 4 ✅
Hint: Boat = (Down + Up)/2; Stream = (Down - Up)/2.
Common Mistakes: Confusing downstream/upstream speeds or averaging the two speeds incorrectly.
2. A man rows downstream at 10 km/h and upstream at 6 km/h. Find his speed in still water.
easy
A. 7 km/h
B. 8 km/h
C. 9 km/h
D. 10 km/h

Solution

  1. Step 1: Identify downstream & upstream speeds

    Downstream = 10 km/h; Upstream = 6 km/h.

  2. Step 2: Compute still water speed

    Boat speed = (10 + 6) ÷ 2 = 8 km/h.

  3. Final Answer:

    Speed in still water = 8 km/h → Option B.

  4. Quick Check:

    Stream = (10 - 6) ÷ 2 = 2; 8 + 2 = 10, 8 - 2 = 6 ✅
Hint: Add and half for boat speed; subtract and half for stream speed.
Common Mistakes: Taking the simple average without considering downstream/upstream relation.
3. The speed of a boat in still water is 9 km/h, and the stream speed is 2 km/h. Find the time to go 22 km downstream.
easy
A. 2 h
B. 2.2 h
C. 2.4 h
D. 2.5 h

Solution

  1. Step 1: Compute downstream speed

    Downstream = Boat + Stream = 9 + 2 = 11 km/h.

  2. Step 2: Time = Distance ÷ Speed

    Time = 22 ÷ 11 = 2 hours.

  3. Final Answer:

    Time required = 2 hours → Option A.

  4. Quick Check:

    11 × 2 = 22 km ✅
Hint: Downstream = boat + stream; then use D ÷ S.
Common Mistakes: Using boat speed (9) instead of effective downstream speed (11).
4. A man can row 30 km downstream in 3 hours and the same distance upstream in 5 hours. Find the speed of the stream.
medium
A. 1 km/h
B. 3 km/h
C. 2 km/h
D. 4 km/h

Solution

  1. Step 1: Compute downstream & upstream speeds

    Downstream = 30 ÷ 3 = 10 km/h; Upstream = 30 ÷ 5 = 6 km/h.

  2. Step 2: Stream speed = (Down - Up) ÷ 2

    Stream = (10 - 6) ÷ 2 = 2 km/h.

  3. Final Answer:

    Stream speed = 2 km/h → Option C.

  4. Quick Check:

    Boat speed = (10 + 6) ÷ 2 = 8 km/h; 8 ± 2 → 10 & 6 ✅
Hint: Stream = (D - U) ÷ 2; Boat = (D + U) ÷ 2.
Common Mistakes: Swapping formulas for boat and stream speeds.
5. A boat can travel 18 km downstream in 2 hours and the same distance upstream in 3 hours. Find the boat’s speed in still water and the speed of the stream.
medium
A. 7 & 2 km/h
B. 8 & 1 km/h
C. 9 & 1.5 km/h
D. 7.5 & 1.5 km/h

Solution

  1. Step 1: Compute downstream & upstream speeds

    Downstream = 18 ÷ 2 = 9 km/h; Upstream = 18 ÷ 3 = 6 km/h.

  2. Step 2: Boat & stream speeds

    Boat = (9 + 6) ÷ 2 = 7.5 km/h; Stream = (9 - 6) ÷ 2 = 1.5 km/h.

  3. Final Answer:

    Boat = 7.5 km/h, Stream = 1.5 km/h → Option D.

  4. Quick Check:

    7.5 + 1.5 = 9 (down), 7.5 - 1.5 = 6 (up) ✅
Hint: Boat = (D + U)/2; Stream = (D - U)/2.
Common Mistakes: Averaging the two times instead of using speed formulas.

Mock Test

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