document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=887930>Question 887930</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (Question) Two cyclists start biking from a trailhead at different speeds and times. The second cyclist travels at 10 miles per hour and starts 2 hours after the first cyclist, who is traveling at 6 miles per hour. Once the second cyclist starts biking, how much time will pass before he catches up with the first cyclist? <BR>\n" );
document.write( "(Answer)<BR>\n" );
document.write( "(a)2 hours<BR>\n" );
document.write( "(b)4 1/2 hours<BR>\n" );
document.write( "(c)5 3/4 hours<BR>\n" );
document.write( "(d)6 hours<BR>\n" );
document.write( "(e)7 1/2 hours\r<BR>\n" );
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document.write( "My attempt: \r<BR>\n" );
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document.write( "What is known from the problem-<BR>\n" );
document.write( "Distance formula=<BR>\n" );
document.write( "r*t=d\r<BR>\n" );
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document.write( "1st cyclist: 3 hours and 18 miles ahead 2nd cyclist (0hr, 0mi; 1hr, 6mi; 2hr, 12mi; 3hr, 18mi)\r<BR>\n" );
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document.write( "2nd cyclist: 3 hours and 18 miles behind 1st cyclist (0hr, 0mi; 1hr, 0mi; 2hr, 0mi; 3hr, 0mi)\r<BR>\n" );
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document.write( "Cyclist 2 starts to ride after Cyclist 1 has traveled for 3 hours or 18 miles. <BR>\n" );
document.write( "(1st hour) for 2nd cyclist = 4th hour for 1st cyclist<BR>\n" );
document.write( "1st cyclist after 4hrs = 24 miles<BR>\n" );
document.write( "2nd cyclist after 1hrs = 10 miles<BR>\n" );
document.write( "(2nd hour)<BR>\n" );
document.write( "1st cyclist after 5hrs = 30 miles<BR>\n" );
document.write( "2nd cyclist after 2hrs = 20 miles<BR>\n" );
document.write( "(3rd hour)<BR>\n" );
document.write( "1st cyclist after 6hrs = 36 miles<BR>\n" );
document.write( "2nd cyclist after 3hrs = 30 miles<BR>\n" );
document.write( "(4th hour)<BR>\n" );
document.write( "1st cyclist after 7hrs = 42 miles<BR>\n" );
document.write( "2nd cyclist after 4hrs = 40 miles<BR>\n" );
document.write( "(5th hour) <BR>\n" );
document.write( "1st cyclist after 8hrs = 48 miles<BR>\n" );
document.write( "2nd cyclist after 5hrs = 50 miles\r<BR>\n" );
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document.write( "Choices (c), (d), and (e) are both too  long. <BR>\n" );
document.write( "Choice (a) is too short.<BR>\n" );
document.write( "There for choice (b) is the correct answer. \r<BR>\n" );
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document.write( "Checking the answer:<BR>\n" );
document.write( "(4 1/2th hour)<BR>\n" );
document.write( "1st Cyclist after 7 1/2hrs = 45 miles<BR>\n" );
document.write( "2nd cyclist after 4 1/2hrs = 45 miles\r<BR>\n" );
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document.write( "That's fine. But what is the algebraic formula for this problem? I solved it using the process of elimination from the given answer choices. There must be a faster way?  <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #536921 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=536921\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two cyclists start biking from a trailhead at different speeds and times. The second cyclist travels at 10 miles per hour and starts 2 hours after the first cyclist, who is traveling at 6 miles per hour. Once the second cyclist starts biking, how much time will pass before he catches up with the first cyclist? <BR>\n" );
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document.write( "In 2 hours, the 1st cyclist is 12 miles away (2*6).<BR>\n" );
document.write( "The 2nd cyclist \"gains on\" the 1st are 4 mi/hr (10-6).<BR>\n" );
document.write( "12/4 = 3 hours.<BR>\n" );
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