The speed of a boat in still water is 5 km/hr. If it takes thrice as much time in going 20 km upstream as in going the same distance downstream, find the speed of the stream.
Given, speed of a boat in still water (V) = 5 km/hr
Let speed of the stream be V' km/hr.
time taken to go 20km downstream (t) = distance travelled$$\div$$relative speed of the boat
= $$\frac{20}{V + V'}$$
=$$\frac{20}{5 + V'}$$ hours
time taken to go 20 km upstream (t') = distance travelled$$\div$$relative speed of the boat
= $$\frac{20}{V - V'}$$
= $$\frac{20}{5 - V'}$$ hours
Given that t' = 3*t
$$\Rightarrow \frac{20}{5 - V'} = 3\times \frac{20}{5 + V'}$$
$$\Rightarrow 4V' = 10$$
$$\Rightarrow V' = 2.5$$ km/hr.
So the speed of the stream is 2.5 km/hr.
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