<PRE><B>Question 851788</B>
A boat travels 15km/hr in still water. In travelling 45 km downstream from Town A to Town B, it completes the journey in 75 minutes less than it takes for the return journey. At what speed does the river flow?
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let x=speed of river flow
15+x=speed of boat downstream
15-x=speed of boat upstream
travel time=distance/speed
...
travel time upstream=45/(15-x) (return trip)
travel time downstream=45/(15+x)
75 min=(75/60) hr
{{{45/(15-x)-45/(15+x)=75/60}}}
LCD:(15-x)(15+x)(60)
{{{60*45(15+x)-60*45(15-x)=75(15-x)(15+x)}}}
40500+2700x-40500+2700x=75(225-x^2)
5400x=16875-75x^2
75x^2+5400x-16875=0
divide by 75
x^2+72-225=0
solve for x by quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
a=1, b=72, c=-225
ans:
x=-12.37 (reject)
or
x=12.37
speed of river flow=12.37 km/hr

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