document.write( "Question 1061532: Nora leaves Town A and walks towards Town B at a speed of 100m/min. At the same time , Kate and Lixin walk from Town B towards Town A at a speed of 80mm/min and 75m/min respectively. If Nora meets Lixin 6 minutes after passing Kate, find the distance between Town A and Town B.\r
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Algebra.Com's Answer #676308 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "Nora leaves Town A and walks towards Town B at a speed of 100 m/min. At the same time , Kate and Lixin walk from Town B towards
\n" ); document.write( "Town A at a speed of 80 m/min and 75 m/min respectively. If Nora meets Lixin 6 minutes after passing Kate,
\n" ); document.write( "find the distance between Town A and Town B.
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document.write( "Let L be the distance between the cities and let \"t\" be the time (in minutes) from the start to the moment Nora meets Kate.\r\n" );
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document.write( "The first equation is \r\n" );
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document.write( "100*t + 80*t = L              (1)   (Nora's walked distance + Kate's distance = L at the moment they meet each other)\r\n" );
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document.write( "Also, the time from the start to the moment Nora meets Lixin is (t+6) minutes.\r\n" );
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document.write( "And the second equation is similar to the first one:\r\n" );
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document.write( "100*(t+6) + 75*(t+6) = L.     (2)   (Nora's walking distance + Lixin's distance = L at the moment they meet each other)\r\n" );
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document.write( "Equations (1) and (2) have equal right sides.\r\n" );
document.write( "Hence, their left sides are equal, too:\r\n" );
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document.write( "100*t + 80*t = 100*(t+6) + 75*(t+6).\r\n" );
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document.write( "It is a single equation for one unknown \"t\". Simplify and solve for \"t\":\r\n" );
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document.write( "180*t = 175t + 600 + 450,\r\n" );
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document.write( "180t - 175t = 1050,\r\n" );
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document.write( "5t = 1050,\r\n" );
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document.write( "t =  = 210.\r\n" );
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document.write( "Thus we found the time \"t\" till the first meeting. It is 210 minutes.\r\n" );
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document.write( "Then the distance between the cities, according to the equation (1), is \r\n" );
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document.write( "    100*210 + 80*210 = 37800 meters = 37.8 kilometers.\r\n" );
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document.write( "Answer.  The distance between the cities is 37800 meters, or 37.8 kilometers.\r\n" );
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