document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1150350>Question 1150350</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hi \r<BR>\n" );
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document.write( "To travel 816km train A takes 9 hours more than train B. if the speed of train A is doubled, it takes 4 hours less than train B .\r<BR>\n" );
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document.write( "what is the speed of train B.\r<BR>\n" );
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document.write( "thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #771729 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13209)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=771729\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Algebraically, there are many ways to set up the problem.  Without trying to overthink the problem, it could be set up directly from the given information as follows:<br><BR>\n" );
document.write( "Let A = speed of train A<BR>\n" );
document.write( "Then 2A = speed of train A if its speed is doubled<BR>\n" );
document.write( "Let B = speed of train B<br><BR>\n" );
document.write( "Then<br><BR>\n" );
document.write( "816/A = time train A takes to go 816km<BR>\n" );
document.write( "816/B = time train B takes to go 816km<BR>\n" );
document.write( "816/(2A) = time train A takes to go 816km if its speed is doubled<br><BR>\n" );
document.write( "(1) The time train A takes to go 816km is 9 hours more than the time train B takes to go 816km:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=816%2FA+=+816%2FB%2B9 ALIGN=MIDDLE  ALT=\"816%2FA+=+816%2FB%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(2) The time train A takes to go 816km if its speed is doubled is 4 hours less than the time it takes train B to go 816km:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=816%2F%282A%29+=+816%2FB-4 ALIGN=MIDDLE  ALT=\"816%2F%282A%29+=+816%2FB-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "There are two equations in A and B which you can solve to find the speed of train B; you can solve them by any method you choose.<br><BR>\n" );
document.write( "Since the two equations contain the term 816/B, I would use substitution to get an equation in only A; then after solving that equation for A I can use that value of A in either of the original equations to find B.<br><BR>\n" );
document.write( "I leave it to you to finish the problem by whatever method you choose.<br><BR>\n" );
document.write( "If a formal algebraic solution is not required, then a solution is easily obtained using logical reasoning and a bit of simple mental arithmetic.<br><BR>\n" );
document.write( "At its normal speed, train A takes 9 hours more than train B to make the trip; when its speed is doubled, train A takes 4 hours less than train B.  So doubling the speed of train A shortens the trip by 13 hours.<br><BR>\n" );
document.write( "When the speed of train A is doubled, the time required for the trip is cut in half.  Since doubling the speed saved 13 hours, train A at its normal speed takes 26 hours for the trip.<br><BR>\n" );
document.write( "That means train B takes 26-9 = 17 hours to make the trip.<br><BR>\n" );
document.write( "And that means the speed of train B is 816/17 = 48km/h.<br><BR>\n" );
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