document.write( "Question 1208615: Mary and Murray travel respectively at x and y km/h heading directly towards each other across a distance of 240 km. If both start at 9 a.m. they will meet at noon. If Murray starts at 8 a.m. and Mary starts at 10 a.m. they will meet at 12:30 p.m. Find (x, y) \n" ); document.write( "

Algebra.Com's Answer #846985 by ikleyn(52778) $\"\"$ $\"About$

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\n" ); document.write( "Mary and Murray travel respectively at x and y km/h heading directly towards each other across a distance of 240 km.
\n" ); document.write( "If both start at 9 a.m. they will meet at noon. If Murray starts at 8 a.m. and Mary starts at 10 a.m. they will meet at 12:30 p.m.
\n" ); document.write( "Find (x, y)
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document.write( "In the first scenario, they travel 3 hours, each.\r\n" );
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document.write( "It gives this total distance equation\r\n" );
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document.write( "    3x + 3y = 240  kilometers.\r\n" );
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document.write( "In the second scenario, Mary travels 2.5 hours, Murray travels 4.5 hours.\r\n" );
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document.write( "It gives this total distance equation\r\n" );
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document.write( "    2.5x + 4y = 240  kilometers.\r\n" );
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document.write( "So, we have this system of equations\r\n" );
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document.write( "    3x    + 3y    = 240,     (1)\r\n" );
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document.write( "    2.5x + 4.5y = 240.    (2)\r\n" );
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document.write( "To solve, from equation (1) express  y =  = 80-x and substitute it into equation (2).  \r\n" );
document.write( "You will get\r\n" );
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document.write( "    2.5x   + 4.5(80-x)  = 240,\r\n" );
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document.write( "    2.5x + 360 - 4.5x = 240,\r\n" );
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document.write( "    2.5x - 4.5x = 240 - 360\r\n" );
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document.write( "    -2x = -120,\r\n" );
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document.write( "      x =  = 60.\r\n" );
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document.write( "Then y = 80-x = 80 - 60 = 20.\r\n" );
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document.write( "ANSWER.  (x,y) = (60,20).\r\n" );
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\n" ); document.write( "\n" ); document.write( "        Normally, this problem is to be solved using system of two equations in two unknown.\r
\n" ); document.write( "\n" ); document.write( "        But it can be solved MENTALLY, too, as an arithmetic word problem, without using equations,
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document.write( "In the first scenario, Mary and Murray travel 3 hours toward each other.  \r\n" );
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document.write( "Hence, their approaching rate is  240/3 = 80 kilometers per hour.\r\n" );
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document.write( "In the second scenario, Murray moves alone during 2 hours from 8 am to 10 am,\r\n" );
document.write( "and after that, they move 2.5 hours together toward each other.\r\n" );
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document.write( "In these 2.5 hours, the distance between them decreases by 2.5*80 = 200 kilometers.\r\n" );
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document.write( "It means that the distance which Murray travels alone in 2 hours from 8:00 am  to  10:am  is \r\n" );
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document.write( "        240-200 = 40 kilometers .\r\n" );
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document.write( "Hence, the Murray' speed is 40/2 = 20 km/h.\r\n" );
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document.write( "Then the Mary' speed is 80-20 = 60 km/h.\r\n" );
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document.write( "ANSWER.  Mary' speed is 60 km/h;  Murray' speed is 20 km/h.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved in two different ways, for your better understanding.\r
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