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The Hudson River flows at a rate of 3 miles per hour. A patrol boat travels 60 miles upriver, and returns in a total time of 9 hours. What is the speed of the boat in still water? \r
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\n" ); document.write( "Let the speed of the boat in still water be \"b\"
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\n" ); document.write( "Upriver DATA:
\n" ); document.write( "distance = 60 mi ; rate = b-3 mph ; time = d/r = 60/(b-3) hrs.
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\n" ); document.write( "Downriver DATA:
\n" ); document.write( "distance = 60 mi; rate = b+3 ; time = d/r = 60/(b+3) hrs.
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\n" ); document.write( "EQUATION:
\n" ); document.write( "time up + time down = 9 hrs
\n" ); document.write( "60/(b-3) + 60/(b+3) = 9
\n" ); document.write( "Divide thru by 60 to get:
\n" ); document.write( "1/(b-3) + 1/(b+3) = 3/20
\n" ); document.write( "Multiply thru by 20(b-3)(b+3) to get:
\n" ); document.write( "20(b+3) + 20(b-3) = 3(b^2-9)
\n" ); document.write( "40b=3b^2-27
\n" ); document.write( "3b^2-40b-27=0
\n" ); document.write( "b=[40+-sqrt(40^2-4*3*-27)]/6
\n" ); document.write( "b=[40+-2sqrt(491)]/6
\n" ); document.write( "Positive Answer: b=14.0528 mph (this is the speed of the boat in still water)
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \r
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