document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=325143>Question 325143</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This word problem has driven me crazy for a week. Please help me and show me how you came up with the answer.\r<BR>\n" );
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document.write( "Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 40 m.p.h. and Train B is traveling at 50 m.p.h.<BR>\n" );
document.write( "Train A passes a station at 6:10 p.m.<BR>\n" );
document.write( "If train B passes the same station at 6:40, at what time will Train B catch up to Train A ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #232835 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=232835\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Trains A and B travel in the same direction on different tracks.\r<BR>\n" );
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document.write( "Trains A is traveling at 40 mph.<BR>\n" );
document.write( "Train B is traveling at 50 mph.\r<BR>\n" );
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document.write( "Train A passes a station at 6:10 pm.<BR>\n" );
document.write( "Train B passes the same station at 6:40 pm.\r<BR>\n" );
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document.write( "When will train B catch up with train A.\r<BR>\n" );
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document.write( "This is a rate * time = distance type of problem.\r<BR>\n" );
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document.write( "The rates will be given.<BR>\n" );
document.write( "The distance will be the same for both trains.<BR>\n" );
document.write( "The time will be different for both trains as shown below:\r<BR>\n" );
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document.write( "Since train A passes the station at 6:10 pm and train B passes the station at 6:40 pm, then train A will have traveled 1/2 hours more than train B.\r<BR>\n" );
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document.write( "If we let T = the time that train B travels, then the time that train A travels is T + .5\r<BR>\n" );
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document.write( "Formula for train A:\r<BR>\n" );
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document.write( "rate * time = distance<BR>\n" );
document.write( "rate = 40<BR>\n" );
document.write( "time = T + .5<BR>\n" );
document.write( "distance = D\r<BR>\n" );
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document.write( "Formula for train A becomes:\r<BR>\n" );
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document.write( "40 * (T + .5) = D\r<BR>\n" );
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document.write( "Formula for train B:\r<BR>\n" );
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document.write( "rate * time = distance<BR>\n" );
document.write( "rate = 50<BR>\n" );
document.write( "time = T<BR>\n" );
document.write( "distance = D\r<BR>\n" );
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document.write( "Formula for train B becomes:\r<BR>\n" );
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document.write( "50 * T = D\r<BR>\n" );
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document.write( "You need to solve these two equations simultaneously to get your answer.\r<BR>\n" );
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document.write( "The formulas are:\r<BR>\n" );
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document.write( "40 * (T + .5) = D<BR>\n" );
document.write( "50 * T = D\r<BR>\n" );
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document.write( "Simplification of these two equations results in:\r<BR>\n" );
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document.write( "40*T + 40*.5 = D<BR>\n" );
document.write( "50*T = D\r<BR>\n" );
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document.write( "Simplify further to get:\r<BR>\n" );
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document.write( "40*T + 20 = D<BR>\n" );
document.write( "50*T = D\r<BR>\n" );
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document.write( "Subtract the first equation from the second equation to get:<BR>\n" );
document.write( "10*T - 20 = 0<BR>\n" );
document.write( "Add 20 to both sides of the equation to get:<BR>\n" );
document.write( "10*T = 20<BR>\n" );
document.write( "Divide both sides of the equation by 10 to get:<BR>\n" );
document.write( "T = 2\r<BR>\n" );
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document.write( "You now know what T is.\r<BR>\n" );
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document.write( "If you substitute 2 for T in both equations you will get:\r<BR>\n" );
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document.write( "40*2.5 = D<BR>\n" );
document.write( "50*2 = D\r<BR>\n" );
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document.write( "Solve for D to get:<BR>\n" );
document.write( "40*2.5 = 100<BR>\n" );
document.write( "50*2 = 100\r<BR>\n" );
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document.write( "D = 100 in both cases as it should.\r<BR>\n" );
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document.write( "The question is what time does train B catch up with train A.\r<BR>\n" );
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document.write( "Train B has passed the station at 6:40 pm.\r<BR>\n" );
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document.write( "Add 2 hours to that and you get 8:40 pm as the time that train B catches up with train A.\r<BR>\n" );
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document.write( "Train A has passed the station at 6:10 pm.\r<BR>\n" );
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document.write( "Add 2.5 hours to that and you get 8:40 pm as the time that train B catches up with train A.\r<BR>\n" );
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