Question 696790
A fisherman can row a boat 8km downstream and return in 100min. If the speed of the stream is 2km per hour, find the speed of the boat in still water?
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let x=speed of boat in still water
x+2=downstream speed
x-2=upstream speed
speed=distance/travel time
8/(x+2)+8/(x-2)=100/60
LCD:(x+2)(x-2)
8(x-2)+8(x+2)=(100/60)*(x+2)(x-2)
8(x-2+x+2)=100(x+2)(x-2)/60
240(2x)=100(x^2-4)
480x=100x^2-400
100x^2-480x-400=0
10x^2-48x-40=0
solve by following quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
a=10, b=-48,c=-40
ans: x≈5.52
speed of boat in still water≈5.52 km/hr