Master Relative Speed in water. Learn to juggle B (Boat) and S (Stream) without confusion.
<p>Imagine the river as a moving walkway (escalator) at an airport.</p>
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<strong style="color: #047857;">DOWNSTREAM (With Flow)</strong>
<p>You run on a moving walkway going your way.</p>
<p>ЁЯЪА <strong>Speed = You + Walkway</strong></p>
<p>(Effortless speed)</p>
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<strong style="color: #b91c1c;">UPSTREAM (Against Flow)</strong>
<p>You run UP the down-escalator.</p>
<p>ЁЯРМ <strong>Speed = You - Walkway</strong></p>
<p>(Struggle to move)</p>
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<p style="margin-top: 10px;"><strong>Rule:</strong> Downstream Speed (D) is ALWAYS > Upstream Speed (U).</p>
<p>Most students solve simultaneous equations. <strong>Don't be them.</strong></p>
<p><strong>Think Visually:</strong> Boat speed (B) is exactly in the MIDDLE of Down (D) and Up (U).</p>
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U <---- [ Stream S ] ---- <strong>B</strong> ---- [ Stream S ] ----> D
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<p>If D = 20 and U = 10:</p>
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<li><strong>B</strong> is the average: (20+10)/2 = <strong>15</strong>.</li>
<li><strong>S</strong> is the gap: 20 - 15 = <strong>5</strong>.</li>
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<p><strong>Scenario:</strong> "It takes 3 times longer to row Up than Down".</p>
<p><strong>The Mental Hack:</strong></p>
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<li>Time Ratio (U:D) = 3:1</li>
<li>So Speed Ratio (U:D) = 1:3 (Inverse relation)</li>
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<p>Now apply Model 2:</p>
<p>U = 1 unit, D = 3 units.</p>
<p><strong>B</strong> = Midpoint = 2 units.</p>
<p><strong>S</strong> = Gap = 1 unit.</p>
<p><strong>Result:</strong> Boat is 2x faster than Stream (Ratio 2:1). Solved without 'x'.</p>
<p><strong>The Trap:</strong> "Boat goes at 10 kmph, returns at 5 kmph. Average speed is 7.5?"</p>
<p><strong>NO!</strong> <span style="color: red; font-weight: bold;">тЭМ</span></p>
<p>For equal distances, Average Speed is <span style="background: #fffbeb; padding: 2px 5px; border-radius: 4px; border: 1px solid #fcd34d;">Harmonic Mean</span>:</p>
<p><strong>Avg = <span class='frac'><span class='num'>2 ├Ч D ├Ч U</span><span class='den'>D + U</span></span></strong></p>
<p>Avg = (2├Ч10├Ч5) / 15 = 100/15 = <strong>6.66 kmph</strong>.</p>