The speed of a boat in still water is ^@16 \text { km/hour }^@. | Math Question and Answer

Answer:

4 km/hour

Step by Step Explanation:

Let the speed of stream be $x \text{ km/hour}$ .
Thus,
Downstream speed = $(16 + x) \text{ km/hour}$
Upstream speed = $(16 - x) \text { km/hour}$
Its is given that, total time taken = $8 \text{ hours}$
So, $\begin{aligned} & { 60 \over 16 - x } + { 60 \over 16 + x} = 8 \\ \implies & { 60 ( 16 + x) + 60 (16 - x) \over (16 - x) (16 + x) } = 8 \\ \implies & { 1920 \over 256 - x^2 } = 8 \\ \implies & { 240 \over 256 - x^2 } = 1 \\ \implies & x^2 = 256 - 240 = 16 \\ \implies & x = 4 \text { km/hour} \end{aligned}$
Hence, the speed of the stream is $\bf 4 \text{ km/hour}.$

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