The speed of a stream is 9 km/h. A boat can go 28 km downstream and 20 km upstream in 8 hours. What is the speed (in km/h) of the boat in still water?

Correct option is C

Given:
Speed of the stream = 9 km/h.
Downstream distance = 28 km.
Upstream distance = 20 km.
Total time = 8 hours.
Formula Used:
Downstream speed = Speed of boat in still water + Speed of stream.
Upstream speed = Speed of boat in still water - Speed of stream.
​$$\text{Time} = \dfrac{\text{Distance}}{\text{Speed}}$$​​
Solution:
Let the speed of the boat in still water be x km/h.
Downstream speed = x + 9.
Upstream speed = x - 9.
Time taken to travel downstream = $$\dfrac{28}{x+9}$$​​

Time taken to travel upstream  = $$\dfrac{20}{x-9}$$​​
Total time = Time downstream + Time upstream = 8 hours.
​$$\begin{aligned}&\Rightarrow \dfrac{28}{x+9} + \dfrac{20}{x-9} = 8 \\&\Rightarrow \dfrac{28(x-9) + 20(x+9)}{(x+9)(x-9)} = 8 \\&\Rightarrow \dfrac{28x - 252 + 20x + 180}{x^2 - 81} = 8 \\&\Rightarrow \dfrac{48x - 72}{x^2 - 81} = 8 \\&\Rightarrow 48x - 72 = 8(x^2 - 81) \\&\Rightarrow 48x - 72 = 8x^2 - 648 \\&\Rightarrow 8x^2 - 48x - 576 = 0 \\&\Rightarrow x^2 - 6x - 72 = 0 \\&\Rightarrow x^2 - 12x + 6x - 72 = 0 \\&\Rightarrow x(x-12) + 6(x-12) = 0 \\&\Rightarrow (x-12)(x+6) = 0 \\&\Rightarrow x = 12 \; \text{or} \; x = -6\end{aligned}$$​​
Since speed cannot be negative, x = 12 km/h.
The speed of the boat in still water is 12 km/h.