document.write( "Question 1130701: Two boats leave the dock at 1:00pm. Each boat travels in a straight line at a constant speed, and the two lines along which the boats are traveling are perpendicular to one another. At 3:00pm, the boats are 16 miles apart. If the first boat travels 6 miles per hour faster than the second, find the speed of each boat. \n" ); document.write( "

Algebra.Com's Answer #747340 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "If the speed of the slower boat is  \"r\"  miles per hour, then the speed of the faster boat is  (r+6) miles per hour.\r\n" );
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document.write( "You have the right angle triangle with the legs  2r  and  2*(r+6)  miles.\r\n" );
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document.write( "The hypotenuse is 16 miles, which gives you an equation\r\n" );
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document.write( "(2r)^2 + (2*(r+6))^2 = 16^2\r\n" );
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document.write( "4r^2 + 4r^2 + 48 r + 144 = 256\r\n" );
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document.write( "8r^2 + 48r - 112 = 0\r\n" );
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document.write( "r^2 + 6r - 14 = 0\r\n" );
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document.write( " =  = .\r\n" );
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document.write( "The only meaningful solution is the positive root  r =  = 1.796 miles per hour.\r\n" );
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document.write( "Answer.  1.796 mph for the slower boat and  7.796 mph for the faster boat.\r\n" );
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document.write( "Check.    = 256.0 = 16^2.    ! Correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "Be aware !. The equation $\"r%5E2%2B%28r%2B6%29%5E2=16%5E2\"$ by @josgarithmetic from his post is W R O N G.\r
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\n" ); document.write( "\n" ); document.write( "O-o-o ! He just re-wrote it correctly from my post !\r
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