document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=816679>Question 816679</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A can run 2 km in 4 min 20 seconds, while B can run this distance in 4 min 34 sec. By how much distance can A beat B? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #491654 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=491654\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A runs 2 km in 4 minutes 20 seconds.<BR>\n" );
document.write( "B runs 2 km in 4 minutes 34 seconds.<BR>\n" );
document.write( "4 minutes 20 seconds is equivalent to 260 seconds.<BR>\n" );
document.write( "4 minutes 34 seconds is equivalent to 274 seconds.<BR>\n" );
document.write( "2 km is equal to 2000 meters.<BR>\n" );
document.write( "the average speed of A is 2000 meters / 260 seconds which is equal to 7.692307692 meters per second.<BR>\n" );
document.write( "the average speed of B is 2000 meters / 274 seconds which is equal to 7.299270073 meters per second.<BR>\n" );
document.write( "in the time that A has run 2000 meters, B has run 7.299270073 meters per second times 260 seconds which means that B has run 1897.810219 meters.<BR>\n" );
document.write( "this means that A has beat B by 2000 - 1897.810219 = 102.189781 meters.\r<BR>\n" );
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document.write( "the basic equation is rate * time = distance.<BR>\n" );
document.write( "what you want to know in this problem is the rate that A and B each run at.<BR>\n" );
document.write( "if rate * time = distance, then rate = distance / time.<BR>\n" );
document.write( "what's what was determined above when i divided the distance that each ran by the time it took each to run it.<BR>\n" );
document.write( "once you know the rate that each person runs at, then you can determine the distance that each runs at in the same amount of time.<BR>\n" );
document.write( "since A was the faster person, you use the time that A used to run the 2000 meters and then figure out the distance that B ran in the same amount of time.\r<BR>\n" );
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document.write( "A runs 2000 meters in 260 seconds.<BR>\n" );
document.write( "B runs 1897.810219 meters in 274 seconds.\r<BR>\n" );
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document.write( "you can also look at this as a ratio problem.<BR>\n" );
document.write( "If B runs 2000 meters in 274 seconds, then how far has B run in 260 seconds.<BR>\n" );
document.write( "your ratio would be:<BR>\n" );
document.write( "2000 / 274 = x / 260<BR>\n" );
document.write( "you would cross multiply to get 2000 * 260 = 274 * x<BR>\n" );
document.write( "simplify that to get 520,000 = 274 * x<BR>\n" );
document.write( "solve for x and you get x = 520,000 / 274 = 1897.810219 meters.<BR>\n" );
document.write( "then you just take the difference between 2000 and 1897.810219 to get 102.189781.\r<BR>\n" );
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