document.write( "Question 1051554: Two trackmen are running on a circular race track 300 ft. in circumference. Running in opposite directions, they meet every 10 seconds. Running in the same direction; the faster passes the slower every 50 seconds. Find their rates in feet per second. \n" ); document.write( "

Algebra.Com's Answer #667011 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "Two track-men are running on a circular race track 300 ft. in circumference. Running in opposite directions,
\n" ); document.write( "they meet every 10 seconds. Running in the same direction; the faster passes the slower every 50 seconds.
\n" ); document.write( "Find their rates in feet per second.
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document.write( "Let their rates are \"u\" and \"v\" ft per second, where \"u\" stands for the faster track-man.\r\n" );
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document.write( "Then the first equation is \r\n" );
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document.write( " = u + v.          (1)\r\n" );
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document.write( "This equation is for the case when they are running in opposite directions.\r\n" );
document.write( "     (Paradoxically, moving in opposite directions means moving towards each other along the circumference in this case !)\r\n" );
document.write( "The left side says that they together cover 300 ft in 10 seconds.\r\n" );
document.write( "The right side is the rate of decreasing the distance between them measured along the circumference. \r\n" );
document.write( "   (Thinking on this equation, keep in mind that they meet for every circle counting after the first meeting).\r\n" );
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document.write( "So the first equation is \r\n" );
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document.write( "u + v = 30.             (1')\r\n" );
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document.write( "The second equation is \r\n" );
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document.write( " = 300.    (2)\r\n" );
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document.write( "This equation is for the case they are running in one direction, and the equation says that for the faster track-man \r\n" );
document.write( "the path from one meeting point to the next meeting point is in one full circumference longer than for the slower track-man.\r\n" );
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document.write( "The equation (2) is equivalent to\r\n" );
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document.write( "u - v = 6.         (2')\r\n" );
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document.write( "The equations (1') and (2') are the governing equations, and we can easily solve them by adding. Doing so, you get\r\n" );
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document.write( "2u = 30 + 6  --->  2u = 36   --->  u =  = 18.\r\n" );
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document.write( "So the faster track-man speed is 18 ft/s.\r\n" );
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document.write( "Then the slower track-man speed is 30-18 = 12 ft/s.\r\n" );
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document.write( "Check.   =  = 10 seconds.\r\n" );
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document.write( "         =  = 50 seconds.\r\n" );
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document.write( "Answer.  18 ft/s  and  12 ft/s.\r\n" );
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