Europe
The speed of a boat in still water is ^@16 \text { km/hour }^@. It goes ^@60 \text { km }^@ upstream and return downstream to starting point in ^@8 \text { hours }^@. Find the speed of the stream.
Answer:
4 km/hour
- 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}.^@
