document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=3173>Question 3173</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A train leaves a station and travels west at 54mph. Four hours later, a second train leaves the same station and travels west at 90mph. When will the second train overtake the first? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #1575 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=1575\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Amberlemon's work is very wrong. Ignore it. Just by looking at the solution...after 8 hours, train 1 will have gone 54*8=432miles. In 4 hours, train2 will have gone 90*4=360miles.\r<BR>\n" );
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document.write( "Besides this, the structure of the basic equations are so wrong. Anyway, here is a correct solution:\r<BR>\n" );
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document.write( "Definitions:\r<BR>\n" );
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document.write( "Let s = speed of train<BR>\n" );
document.write( "Let d = distance travelled<BR>\n" );
document.write( "Let t = time travelled by first train<BR>\n" );
document.write( "Let T = time travelled by second train.\r<BR>\n" );
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document.write( "Formula relating these is s = d/t or s=d/T\r<BR>\n" );
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document.write( "Now, for train1: 54 = d/t and train2: 90 = d/T... both have the same distance d, since we want to find the time when they meet, ie have travelled the same distance.\r<BR>\n" );
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document.write( "We can re-arrange these to give:<BR>\n" );
document.write( "54t = d and<BR>\n" );
document.write( "90T = d\r<BR>\n" );
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document.write( "Since both have d, we can equate the 2 equations and say that 54t = 90T.\r<BR>\n" );
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document.write( "How about relating t and T?, well, we know that T = t-4, so put this into the second equation.\r<BR>\n" );
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document.write( "54t = 90(t-4)<BR>\n" );
document.write( "54t = 90t - 360<BR>\n" );
document.write( "36t = 360<BR>\n" );
document.write( "so t=10 hours.\r<BR>\n" );
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document.write( "So train 2 will take over the first when train1 has been travelling for 10 hours. Or when train2 has been travelling for (10-4) --> 6hours.\r<BR>\n" );
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document.write( "Check: in 10 hours, train1 (10*54) --> travels 540 miles.<BR>\n" );
document.write( "in 6 hours, train2 travels ( 6*90) --> 540 miles.\r<BR>\n" );
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document.write( "jon<BR>\n" );
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