document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=971429>Question 971429</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A takes 45 seconds to run a lap and every 25 seconds, B who is running in the opposite direction passes A. how long does it take B to run a lap? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #593919 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=593919\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A takes 45 seconds to do a lap.<BR>\n" );
document.write( "B passes A every 25 seconds.<BR>\n" );
document.write( "if you look at the first lap only, B will pass A after 25 seconds have elapsed.<BR>\n" );
document.write( "this means that A has run 25/45 of the lap while B has only run 20/45 of the lap.<BR>\n" );
document.write( "B has to be running slower than A.<BR>\n" );
document.write( "the ratio of B's speed to A's speed is therefore 20/45 divided by 25/45 = 20/25 = 4/5.<BR>\n" );
document.write( "B is running at 4/5 the speed of A.<BR>\n" );
document.write( "rate * time = distance.<BR>\n" );
document.write( "time for A is 45 seconds.<BR>\n" );
document.write( "distance for A is 1 lap.<BR>\n" );
document.write( "rate for A is determined by the equation of r*t = d which becomes r*45 = 1 which becomes 1/45.<BR>\n" );
document.write( "the rate of A is 1/45.<BR>\n" );
document.write( "the rate of B is only 4/5 that, so the rate of B has to be 4/5 * 1/45 = 4/225.<BR>\n" );
document.write( "the rate of B is 4/225.<BR>\n" );
document.write( "rate * time = distance.<BR>\n" );
document.write( "4/225 * t = 1<BR>\n" );
document.write( "t = 225/4 = 56.25 seconds.\r<BR>\n" );
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document.write( "A takes 45 seconds.<BR>\n" );
document.write( "B takes 56.25 seconds.\r<BR>\n" );
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document.write( "it's really hard to show but i think it's correct.\r<BR>\n" );
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document.write( "let's assume that A is running at 5 yards a second and B is running at 4 yards a second.\r<BR>\n" );
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document.write( "A will run 1 lap in 45 seconds which is equal to 5*45 = 225 yards.<BR>\n" );
document.write( "B will run 1 lap in 56.25 seconds which is equal to 4 * 56.25 = 225 yards.\r<BR>\n" );
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document.write( "so one lap is equal to 225 yards.\r<BR>\n" );
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document.write( "we'll look at the position around the track of A and B every 25 seconds.\r<BR>\n" );
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document.write( "in 25 seconds, A will be at the 25/45 * 225 = 125 yard mark.<BR>\n" );
document.write( "in the same 25 seconds, B will be at the 25/56.25 * 225 = 100 yard mark.<BR>\n" );
document.write( "since A is running in the opposite direction from B, then B is at the 225 - 100 = 125 yard mark of A.<BR>\n" );
document.write( "in other words, they pass each other at the 25 second mark.\r<BR>\n" );
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document.write( "in 50 seconds, A will be at the 50/45 * 225 = 250 yard mark.<BR>\n" );
document.write( "since the track is only 225 yards, then A has done 1 lap and is at the 25 yard mark of his second lap.<BR>\n" );
document.write( "in the same 50 seconds, B will be at the 50/56.25 * 225 = 200 yard mark of his first lap.<BR>\n" );
document.write( "since they are traveling in opposite directions, B's 200 yard mark is really A's 25 yard mark, so they pass each other again.\r<BR>\n" );
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document.write( "in 75 seconds, A will be at the 75/45 * 225 = 375 yard mark.<BR>\n" );
document.write( "since the track is only 225 yards, then A is at the 375 - 225 = 150 yard mark of his second lap.<BR>\n" );
document.write( "in the same 75 seconds, B will be at the 75/56.25 * 225 = 300 yard mark.<BR>\n" );
document.write( "since the track is only 225 yards, then B is at the 300 - 225 = 75 yard mark of his second lap.<BR>\n" );
document.write( "since B is traveling in the opposite direction as A, then B's 75 yard mark is really A's 225 - 75 = 150 yard mark.<BR>\n" );
document.write( "they are passing each other again at A's 150 yard mark.\r<BR>\n" );
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document.write( "this continues and repeats every 25 seconds.\r<BR>\n" );
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document.write( "we can go on forever, but we should be able to see that they will pass each other every 25 seconds.\r<BR>\n" );
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document.write( "take any 25 second periods and you will see that they are at the same position relative to each other.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "assume that 300 seconds have elapsed.\r<BR>\n" );
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document.write( "A will have traveled 300/45 * 225 = 1500 yards.<BR>\n" );
document.write( "since the track is only 225 yards, then A is at his 150 yard mark in his seventh lap.  6 laps is 6 * 225 = 1350 yards + 150 = 1500 yards.\r<BR>\n" );
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document.write( "B will have traveled 300/56.25 * 225 = 1200 yards.<BR>\n" );
document.write( "since the track is only 225 yards, then B is at his 75 yard mark in his 6th lap.<BR>\n" );
document.write( "5 laps is 5 * 225 = 1125 yards + 75 = 1200 yards.\r<BR>\n" );
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document.write( "since B is running in the opposit3e direction from A, then he is at the 225 - 75 = 150 yards mark of A.\r<BR>\n" );
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document.write( "they are at the same position in the track after 300 seconds which means they are just passing each other again.\r<BR>\n" );
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document.write( "i believe your solution is that it will take B 56.25 seconds to complete one lap.\r<BR>\n" );
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document.write( "he is running at 4/5 the speed that A is running at.\r<BR>\n" );
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document.write( "it took him 25 seconds to run the same distance that it took A 20 seconds to run.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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