document.write( "Question 1148210: Stu trained for a triathlon for 5 hours yesterday. He ran 5 miles and then biked 80 miles. His biking speed is 15 mph faster than his running speed. What is his running speed? \n" ); document.write( "

Algebra.Com's Answer #769573 by ikleyn(52903) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Based on the given data, I can guess the answer in 5 seconds.\r\n" );
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document.write( "    His running speed is 5 miles per hour.\r\n" );
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document.write( "CHECK.  He spent 1 hour running and  = 4 hours biking.\r\n" );
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\n" ); document.write( "\n" ); document.write( "But if you want ALGEBRA solution, here it is.\r
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document.write( "Let x be the running speed, which is the value under the question.\r\n" );
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document.write( "Then his biking speed is  (x+15) miles per hour.\r\n" );
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document.write( "The time spent running is    hours.\r\n" );
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document.write( "The time spent biking is  .\r\n" );
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document.write( "The total time is 5 hours; it gives you and equation\r\n" );
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document.write( "     +  = 5   hours.\r\n" );
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document.write( "It is so called \"time\" equation.\r\n" );
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document.write( "As soon as you got it, the setup is just completed.\r\n" );
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document.write( "Now your task is to solve it.\r\n" );
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document.write( "For it, multiply both sides by x*(x+15).  You will get\r\n" );
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document.write( "    5*(x+15) + 80x = 5x*(x+15)\r\n" );
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document.write( "    (x+15)   + 16x = x*(x+15)\r\n" );
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document.write( "    17x + 15       = x^2 + 15x\r\n" );
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document.write( "     x^2 - 2x - 15 = 0\r\n" );
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document.write( "     (x-5)*(x+3)    = 0\r\n" );
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document.write( "Of the two roots, x= 5  and  x= -3, only positive x= 5 makes sense.\r\n" );
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document.write( "So, your answer is:  the running speed is  5 mph;  same as I guessed at the beginning.\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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