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Jen’s boat cruised 45 miles upstream and 45 miles back in a total of 8 hr. The speed of the river is 3 mph. Find the speed of the boat in still water.
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\n" ); document.write( "You will need to apply the \"distance formula\":
\n" ); document.write( "d = rt
\n" ); document.write( "where
\n" ); document.write( "d is distance
\n" ); document.write( "r is rate or speed
\n" ); document.write( "t is time
\n" ); document.write( ".
\n" ); document.write( "However, for this problem we are going to solve for t:
\n" ); document.write( "d = rt
\n" ); document.write( "d/r = t
\n" ); document.write( "t = d/r
\n" ); document.write( ".
\n" ); document.write( "Let x = speed of boat in still water
\n" ); document.write( "then
\n" ); document.write( "x+3 = speed going downstream
\n" ); document.write( "x-3 = speed going upstream
\n" ); document.write( ".
\n" ); document.write( "\"time going upstream\" + \"time going downstream\" = 8
\n" ); document.write( "45/(x+3) + 45/(x-3) = 8
\n" ); document.write( "multiplying both sides by (x+3)(x-3):
\n" ); document.write( "45(x-3) + 45(x+3) = 8(x+3)(x-3)
\n" ); document.write( "45x - 135 + 45x + 135 = 8(x^2-9)
\n" ); document.write( "90x = 8x^2-72
\n" ); document.write( "0 = 8x^2-90x-72
\n" ); document.write( "0 = 4x^2-45x-36
\n" ); document.write( "Factoring the right:
\n" ); document.write( "0 = (4x+3)(x-12)
\n" ); document.write( "x = {-3/4 , 12}
\n" ); document.write( "Well we can toss out the negative answer leaving:
\n" ); document.write( "x = 12 mph (speed in still water) \n" ); document.write( "