Boats & Streams
Master Relative Speed in water. Learn to juggle B (Boat) and S (Stream) without confusion.
Model 1: The 'Escalator' Analogy
Imagine the river as a moving walkway (escalator) at an airport.
You run on a moving walkway going your way.
ЁЯЪА Speed = You + Walkway
(Effortless speed)
You run UP the down-escalator.
ЁЯРМ Speed = You - Walkway
(Struggle to move)
Rule: Downstream Speed (D) is ALWAYS > Upstream Speed (U).
Model 2: The 'Golden Average' Trick
Most students solve simultaneous equations. Don't be them.
Think Visually: Boat speed (B) is exactly in the MIDDLE of Down (D) and Up (U).
U <---- [ Stream S ] ---- B ---- [ Stream S ] ----> D
If D = 20 and U = 10:
- B is the average: (20+10)/2 = 15.
- S is the gap: 20 - 15 = 5.
Model 3: The 'Ratio Multiplier' (Advanced)
Scenario: "It takes 3 times longer to row Up than Down".
The Mental Hack:
- Time Ratio (U:D) = 3:1
- So Speed Ratio (U:D) = 1:3 (Inverse relation)
Now apply Model 2:
U = 1 unit, D = 3 units.
B = Midpoint = 2 units.
S = Gap = 1 unit.
Result: Boat is 2x faster than Stream (Ratio 2:1). Solved without 'x'.
Trap Alert: 'Average Speed'
The Trap: "Boat goes at 10 kmph, returns at 5 kmph. Average speed is 7.5?"
NO! тЭМ
For equal distances, Average Speed is Harmonic Mean:
Avg = 2 ├Ч D ├Ч UD + U
Avg = (2├Ч10├Ч5) / 15 = 100/15 = 6.66 kmph.
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