document.write( "Question 333302: A boat travels 10km upstream and 10km back. The time for the roundtrip is 5 hours. The speed of the stream is 2km/hour. What is the speed of the boat in still water? \n" ); document.write( "

Algebra.Com's Answer #238825 by mananth(16946) $\"\"$ $\"About$

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let the speed of the boat in still water be x kmph
\n" ); document.write( "speed of current =2kmph
\n" ); document.write( "..
\n" ); document.write( "speed downstream = x+2
\n" ); document.write( "speed upstream = x-2
\n" ); document.write( "..
\n" ); document.write( "distance both ways = 10 km
\n" ); document.write( "time = distance / speed
\n" ); document.write( "..
\n" ); document.write( "time upstream + time downstream = 5 hours
\n" ); document.write( "10/(x+2)+10/(x-2) = 5
\n" ); document.write( "LCM = (x+2)(x-2)
\n" ); document.write( "10(x-2)+10(x+2) / (x-2)(x+2)= 5
\n" ); document.write( "10x-20+10x+20=5(x-2)(x+2)
\n" ); document.write( "20x=5x^2-20
\n" ); document.write( "5x^2-20x-20=0
\n" ); document.write( "divide by 5
\n" ); document.write( "x^2-4x-4=0
\n" ); document.write( "..
\n" ); document.write( "solve by quadratic equation formula
\n" ); document.write( "x= (-b+-sqrt(b^2-4ac))/2a
\n" ); document.write( "a=1,b=-4,c=-4
\n" ); document.write( "b^2-4ac = 16+16=32
\n" ); document.write( "x1=(4+sqrt32) /2
\n" ); document.write( "x1= 4.82 kmph
\n" ); document.write( "..
\n" ); document.write( "x2=(4-sqrt32) /2
\n" ); document.write( "x2= -0.82 ( Ignore)
\n" ); document.write( "the speed of boat in still water = 4.82 km/h
\n" ); document.write( " \n" ); document.write( "

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