document.write( "Question 1150319: Miguel went on a bike ride of 24 miles. He realized that if he had gone 6 mph faster, he would have arrived 9 hours sooner. How fast did he actually ride? \n" ); document.write( "

Algebra.Com's Answer #771708 by ikleyn(52814) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " The way on how @josmiceli solves the problem, may scare the reader.\r
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\n" ); document.write( "\n" ); document.write( " Meanwhile, all such problems have very straightforward SIMPLE LOGIC nice solutions using \"time\" equation.\r
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document.write( "Let v be the unknown rate of the biker.\r\n" );
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document.write( "Then the time of his biking is   hours.\r\n" );
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document.write( "Had he gone 6 miles faster, his time would be   hours.\r\n" );
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document.write( "The time equation is\r\n" );
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document.write( "     -  = 9  hours.\r\n" );
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document.write( "To solve it, multiply both sides by x*(x+6).  You will get\r\n" );
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document.write( "    48*(x+6) - 48x = 9x*(x+6)\r\n" );
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document.write( "    48x + 288 - 48x = 9x^2 + 54x\r\n" );
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document.write( "    9x^2 + 54x - 288 = 0\r\n" );
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document.write( "     x^2 +  6x -  32 = 0\r\n" );
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document.write( "     (x+8)*(x-2)     = 0\r\n" );
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document.write( "The only positive root x= 2 makes sense.\r\n" );
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document.write( "It gives the ANSWER :  the rate of biking is  2 miles per hour.\r\n" );
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document.write( "CHECK.  I will check equation (1) by substituting the value x= 2 there\r\n" );
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document.write( "         -  = 12 - 3 = 9  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
\n" ); document.write( "\n" ); document.write( "From this lesson, learn on how to write, how to use and how to solve a \"time\" equation.\r
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\n" ); document.write( "\n" ); document.write( "To see many other similar solved problems, look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Had a car move faster it would arrive sooner\r
\n" ); document.write( "\n" ); document.write( "    - How far do you live from school? \r
\n" ); document.write( "\n" ); document.write( "    - Earthquake waves \r
\n" ); document.write( "\n" ); document.write( "    - Time equation: HOW TO use, HOW TO write and HOW TO solve it \r
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