The speed of a boat in still water is 11 km/h. It can go 12 km upstream and return downstream to original point in 2 hours 45 minutes. Find the speed of the stream.

Let the speed of the stream be x km/h.

Speed of boat in -

Still water = 11 km/h

Upstream = (11 - x) km/h

Downstream = (11 + x) km/h

Given,

Boat can go 12 km upstream and return downstream to original point in 2 hours 45 minutes.

Converting 2 hours 45 minutes to hours:

2 hours 45 minutes = ((2 x 60) + 45) minutes = 165 minutes.

165 minutes = $\dfrac{165}{60}$ hours

$\therefore \dfrac{12}{11 - x} + \dfrac{12}{11 + x} = \dfrac{165}{60} \\[1em] \Rightarrow \dfrac{12(11 + x) + 12(11 - x)}{(11 + x)(11 - x)} = \dfrac{165}{60} \\[1em] \Rightarrow \dfrac{132 + 12x + 132 - 12x}{121 - x^2} = \dfrac{165}{60} \\[1em] \Rightarrow \dfrac{264}{121 - x^2} = \dfrac{11}{4}\\[1em] \Rightarrow 264 \times 4 = 11(121 - x^2) \\[1em] \Rightarrow 1056 = 1331 - 11x^2 \\[1em] \Rightarrow 11x^2 = 1331 - 1056 \\[1em] \Rightarrow 11x^2 = 275 \\[1em] \Rightarrow x^2 = \dfrac{275}{11} \\[1em] \Rightarrow x^2 = 25 \\[1em] \Rightarrow x^2 - 25 = 0 \\[1em] \Rightarrow (x - 5)(x + 5) = 0 \\[1em] \Rightarrow x = 5, -5$

Since speed cannot be negative hence, x ≠ -5.

Hence, speed of stream is 5 km/h.