1. A boat takes six hours to travel a certain distance downstream and five hours to travel a certain distance upstream. The distance travelled upstream is half of the travelled downstream. If the speed of the current is 4 km/hr, what is the speed of the boat in still water? (in km/hr)
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By: anil on 05 May 2019 01.37 am
Let speed of boat in still water = $$x$$ km/hr Let distance travelled downstream = $$2d$$ km => Distance travelled upstream = $$d$$ km Using, $$time = frac{distance}{speed}$$ => $$6 = frac{2d}{x + 4}$$ ---------(i) and $$5 = frac{d}{x - 4}$$ ---------(ii) Dividing eqn(i) from (ii), we get : => $$frac{6}{5} = frac{frac{2d}{x + 4}}{frac{d}{x - 4}}$$ => $$frac{6}{5} = frac{2 (x - 4)}{x + 4}$$ => $$6x + 24 = 10x - 40$$ => $$10x - 6x = 24 + 40 = 64$$ => $$x = frac{64}{4} = 16$$ km/hr
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