document.write( "Question 1144343: A motorcycle drive travels 15 kph faster than a bicycle rider . The motorcycle drive covers 60 km in two hours than that time it takes the bicycle rider to travel the same distance . What is the mathematical sentence
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Algebra.Com's Answer #765420 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "                A motorcycle driver travels 15 kph faster than a bicycle rider. \r\n" );
document.write( "                The motorcycle driver takes 2 hours less to cover 60 km than it takes the bicycle rider \r\n" );
document.write( "                to travel the same distance. What is the mathematical sentence\r\n" );
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document.write( "Let x be the bicycle average rate, in km/h.\r\n" );
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document.write( "Then the motorcycle average rate is (x+15) km/h, according to the condition.\r\n" );
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document.write( "The bicycle takes  hours to cover the same distance.\r\n" );
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document.write( "The difference of times is 2 hours, as the condition states:\r\n" );
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document.write( "     -  = 2   hours.\r\n" );
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document.write( "It is so called \"time equation\" -- the BASIC equation for such type of problems.\r\n" );
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document.write( "It is the equation -- \"the mathematical sentence\" -- you asked for.\r\n" );
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document.write( "To solve it, multiply both sides by x*(x+15). You will get\r\n" );
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document.write( "    60*(x+15) - 60x = 2x*(x+15).\r\n" );
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document.write( "Simplify and solve for x\r\n" );
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document.write( "     900 = 2x^2 + 30x\r\n" );
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document.write( "     2x^2 + 30x - 900 = 0\r\n" );
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document.write( "     x^2  + 15x - 450 = 0\r\n" );
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document.write( "     (x+30)*(x-15) = 0.\r\n" );
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document.write( "The roots are -30 and 15, but only positive x= 15 makes sense.\r\n" );
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document.write( "So, you get the ANSWER:  the bicycle average rate is 15 km/h;  the motorcycle average rate is 15+15 = 30 km/h.\r\n" );
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document.write( "CHECK.   = 4 hour for the bicycle and   = 2 hours for the motorcycle with the difference 4-2 = 2 hours.   ! Correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "Using \"time\" equation is the STANDARD method of solving such problems.\r
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\n" ); document.write( "\n" ); document.write( "To see many other similar solved problems, look into the lessons\r
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