🚤 Boat and Stream

🔹 Basic Concept

Boat speed in still water = \(B\) km/h Stream speed (current) = \(S\) km/h

Downstream (With Current):
\[ \text{Speed}_{\text{down}} = B + S \]

Upstream (Against Current):
\[ \text{Speed}_{\text{up}} = B - S \]

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

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🧠 Exam Shortcuts & Tricks

Shortcut 1: Always note “Downstream = With Current” → Speed increases

Shortcut 2: Upstream = Against Current → Speed decreases

Shortcut 3: Stream speed = \(\frac{\text{Downstream speed – Upstream speed}}{2}\)

Shortcut 4: Boat speed = \(\frac{\text{Downstream speed + Upstream speed}}{2}\)

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✍️ Solved Examples

Example 1:
Boat speed = 10 km/h, Stream = 2 km/h. Downstream speed = \(10 + 2 = 12\) km/h Upstream speed = \(10 - 2 = 8\) km/h Time to travel 24 km downstream = \( \frac{24}{12} = 2 \) hours Time to travel 24 km upstream = \( \frac{24}{8} = 3 \) hours

Example 2:
Boat takes 1 hour downstream and 2 hours upstream to cover 30 km each way. Find Boat speed (B) and Stream speed (S).
\[ B + S = \frac{30}{1} = 30 \] \[ B - S = \frac{30}{2} = 15 \] \[ \text{Adding: } 2B = 45 \Rightarrow B = 22.5 \text{ km/h} \] \[ S = 30 - 22.5 = 7.5 \text{ km/h} \]

Example 3:
Stream speed unknown. Downstream speed = 18 km/h, upstream speed = 12 km/h. Find Boat speed and Stream speed.
\[ B = \frac{18+12}{2} = 15 \text{ km/h}, \quad S = \frac{18-12}{2} = 3 \text{ km/h} \]

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