document.write( "Question 77446: Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking? \n" ); document.write( "
Algebra.Com's Answer #55559 by Edwin McCravy(20056)\"\" \"About 
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document.write( "Two cyclists start biking from a trail's start 3 hours apart. The second\r\n" );
document.write( "cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist\r\n" );
document.write( "who is traveling at 6 miles per hour. How much time will pass before the second\r\n" );
document.write( "cyclist catches up with the first from the time the second cyclist started\r\n" );
document.write( "biking?\r\n" );
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document.write( "First here's how to work it your head with no algebra! \r\n" );
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document.write( "When the second one starts, the first one is 18 miles down the trail, since he\r\n" );
document.write( "has been going for 3 hours at 6 miles per hour. The second one's approach rate\r\n" );
document.write( "is 10-6 or 4 miles per hour. So in 4 hours he'll have covered 4×4 or 16 of the\r\n" );
document.write( "18 miles between them, so to go the remaining 2 miles between them, approaching\r\n" );
document.write( "by 4 miles per hour, it will take him an additional half hour, so the answer \r\n" );
document.write( "is  4 1/2 hours. \r\n" );
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document.write( "But your teacher will probably not accept that method, although you should be\r\n" );
document.write( "able to think it out that way. Here's the way your teacher probably expects\r\n" );
document.write( "you to do it.\r\n" );
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document.write( "Make this chart:\r\n" );
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document.write( "                    Distance    Rate      Time\r\n" );
document.write( "First bicyclist      \r\n" );
document.write( "Second bicyclist     \r\n" );
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document.write( "Let the answer be t hours.  Then fill in t for the second \r\n" );
document.write( "bicyclist's time.\r\n" );
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document.write( "                    Distance    Rate      Time\r\n" );
document.write( "First bicyclist      \r\n" );
document.write( "Second bicyclist                            t\r\n" );
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document.write( "The first bicyclist travels 3 hours longer than the second,\r\n" );
document.write( "so fill in his time as t+3\r\n" );
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document.write( "                    Distance    Rate      Time\r\n" );
document.write( "First bicyclist                            t+3\r\n" );
document.write( "Second bicyclist                            t\r\n" );
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document.write( "Fill in their rates as 6 and 10 respectively\r\n" );
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document.write( "                    Distance    Rate      Time\r\n" );
document.write( "First bicyclist                   6        t+3\r\n" );
document.write( "Second bicyclist                 10         t\r\n" );
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document.write( "Now use Distance = Rate × Time to fill in the \r\n" );
document.write( "distances.\r\n" );
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document.write( "                    Distance    Rate      Time\r\n" );
document.write( "First bicyclist      6(t+3)       6        t+3\r\n" );
document.write( "Second bicyclist      10t        10         t\r\n" );
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document.write( "Now since they traveled the SAME distance, their\r\n" );
document.write( "distances are equal, so the equation is:\r\n" );
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document.write( "        6(t+3) = 10t\r\n" );
document.write( "       6t + 18 = 10t\r\n" );
document.write( "      6t - 10t = -18    \r\n" );
document.write( "           -4t = -18\r\n" );
document.write( "             t = (-18)/(-4)\r\n" );
document.write( "             t = 18/4 \r\n" );
document.write( "             t = 9/2\r\n" );
document.write( "             t = 4 1/2 hours.\r\n" );
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document.write( "Edwin

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