document.write( "Question 1111099: Two cars, A and B, 148 kilometers apart, traveled toward each other. A started at 6 a.m. while B started an hour later. They met on the road at 9 a.m. Had both of them started at 6 a.m., they would have met at 8:28. Find the speed. \n" ); document.write( "

Algebra.Com's Answer #726117 by ikleyn(52850) $\"\"$ $\"About$

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document.write( "1.  In the first scenario, 1-st car was on the way 3 hours (from 6 am till 9 am) before meeting.\r\n" );
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document.write( "                           2-nd car was on the way 2 hours before meeting.\r\n" );
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document.write( "    Let \"a\" and \"b\" be their rates in miles per MINUTE, respectively. \r\n" );
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document.write( "    Then from the first scenario, the total distance between the cities was\r\n" );
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document.write( "        180a + 120b  = 148  miles.               (1)    (3 hours = 180 minutes;  2 hours = 120 minutes !)\r\n" );
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document.write( "2.  In the second scenario, each car was on the way 2 hours and 28 minutes = 148 minutes.  \r\n" );
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document.write( "    Therefore, the second equation for the entire distance is\r\n" );
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document.write( "        148a + 148b = 148  miles,   or\r\n" );
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document.write( "           a + b = 1       (miles per minute)     (2) \r\n" );
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document.write( "3.  Thus you have this system of two equations in two unknowns\r\n" );
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document.write( "       a +    b =   1,    and\r\n" );
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document.write( "    180a + 120b = 148.\r\n" );
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document.write( "    Solve it by ANY method you want.  Both methods - Substitution and Elimination - are good.  Choose any and complete the solution on your own.\r\n" );
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document.write( "4.   H a p p y   s o l v i n g  ! !\r\n" );
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