If a boat takes 4 hours longer to travel a distance of 45 km upstream than to travel the same distance downstream, then find the speed of the boat in still water if the speed of the stream is 2 km/hour.

Distance $= 45$ km (both upstream and downstream)

Speed of stream $= 2$ km/hour

Upstream takes $4$ hours longer than downstream

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Let speed of boat in still water $= b$ km/hour

Downstream speed $= (b + 2)$ km/hour

Upstream speed $= (b - 2)$ km/hour

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Time downstream $= \dfrac{45}{b + 2}$ hours

Time upstream $= \dfrac{45}{b - 2}$ hours

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Upstream takes $4$ hours longer:

$\dfrac{45}{b - 2} - \dfrac{45}{b + 2} = 4$

$\dfrac{45(b + 2) - 45(b - 2)}{(b - 2)(b + 2)} = 4$

$\dfrac{45b + 90 - 45b + 90}{b^2 - 4} = 4$

$\dfrac{180}{b^2 - 4} = 4$

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$180 = 4(b^2 - 4)$

$180 = 4b^2 - 16$

$196 = 4b^2$

$b^2 = 49$

$b = 7$

Therefore, the speed of the boat in still water is $7$ km/hour.