Algebra.Com's Answer #469295 by Edwin McCravy(20056)![\"\"](\"/images/stars/stars-13.gif\")  
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How to solve this problem please: At the beginning of a bicycle ride for charity, Yady Saldarriaga and Dane McGuckian are 30 mi. apart. If they leave at the same time and ride in the same direction, Yady overtakes DAne in 6 hours. If they ride toward each other, they pass each other in 1 hr. What are their rates?
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document.write( "Let the speed of the faster bike be x mi/hr\r\n" );
document.write( "Let the speed of the slower bike be y mi/hr\r\n" );
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document.write( "Whether the faster catches up to the slower when they are going in the same\r\n" );
document.write( "direction, or whether they ride toward each other and meet, the 30 mile\r\n" );
document.write( "distance between them shinks to zero.\r\n" );
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document.write( "When traveling in the same direction the catch-up rate of the faster bike\r\n" );
document.write( "to the slower bike is at a speed of x-y.\r\n" );
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document.write( "Since time =  , the faster catches up the entire 30 miles\r\n" );
document.write( "head start which the slower one has on the faster in  hours.\r\n" );
document.write( "That is, the 30 miles between them shrinks to zero (by the faster catching up)\r\n" );
document.write( "in \r\n" );
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document.write( "hours, and we are given that that is 6 hours. So we have the equation\r\n" );
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document.write( " = 6\r\n" );
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document.write( "When traveling in opposite directions they approach each other at the speed\r\n" );
document.write( "x+y.\r\n" );
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document.write( "Since time = , the 30 miles between them shrinks to zero (by them \r\n" );
document.write( "meeting each other) in hours, and we are given that that is 1 hour. \r\n" );
document.write( "So we have the equation\r\n" );
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document.write( " = 1\r\n" );
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document.write( "And so we have the system of equations:\r\n" );
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document.write( " = 6\r\n" );
document.write( " = 1\r\n" );
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document.write( "Clearing the first equation of fractions, we have:\r\n" );
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document.write( "30 = 6(x-y)\r\n" );
document.write( "30 = 6x - 6y\r\n" );
document.write( "Divide through by 6\r\n" );
document.write( " 5 = x - y\r\n" );
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document.write( "Clearing the second equation of fractions, we have:\r\n" );
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document.write( "30 = 1(x+y)\r\n" );
document.write( "30 = x + y\r\n" );
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document.write( "Now the system is\r\n" );
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document.write( " 5 = x - y\r\n" );
document.write( "30 = x + y\r\n" );
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document.write( "Adding the two equations term by term, we have:\r\n" );
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document.write( "35 = 2x\r\n" );
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document.write( "Dividing both sides by 2, we have:\r\n" );
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document.write( "17.5 = x\r\n" );
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document.write( "So the faster bike goes at 17.5 mi/hr.\r\n" );
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document.write( "Substituting 17.5 for x in\r\n" );
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document.write( " 5 = x - y\r\n" );
document.write( " 5 = 17.5 - y\r\n" );
document.write( " y = 12.5\r\n" );
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document.write( "So the slower bike goes at 12.5 mi/hr.\r\n" );
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document.write( "Edwin \n" );
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