Question 388616
speed of a boat in still wateris 9km/hr.It goes 12km down stream and comes back to the starting point in 3hrs.What is the speed of water in the stream?
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boat speed = 9 km/h
speed of current = x km/h
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upstream speed = 9-x
downstream speed = 9+x
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time downstream + time upstream = 3 hours
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t=d/r
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{{{12/(9-x)+12/(9+x)=3}}}
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LCD = (9+x)(9-x)
multiply by LCD
{{{(12(9+x)-12(9-x))/((9+x)(9-x))}}}=3
(108+12x-108+12x)=3(9+x)(9-x)
24x=3(81-x^2)
/3
8x=81-x^2
x^2+8x-81=0
find roots x1,x2 by using quadratic formula
discriminant = b^2-4ac = 388
{{{x1=(-8+sqrt(388))/(2)}}}
{{{(highlight(x1=5.85))}}} km/h speed of current
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x2 will be negative so ignore
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m.ananth@hotmail.ca