document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=896107>Question 896107</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if a train runs at 40 kmph it reaches its destination late by 11 minutes. but if it runs at 50 kmph it is late by 5 minutes only. find the distance to be covered by the train<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #543247 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=543247\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let T equal the time that it should take.<BR>\n" );
document.write( "let D = the distance.\r<BR>\n" );
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document.write( "rate * time = distance\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "40(T+11) = D\r<BR>\n" );
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document.write( "50(T+5) = D\r<BR>\n" );
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document.write( "since both expressions on the left side of the equation equal D, you can set these expressions equal to each other to get:\r<BR>\n" );
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document.write( "40(T+11) = 50(T+5)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "40T + 440 = 50T + 250\r<BR>\n" );
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document.write( "subtract 40T from both sides of the equation and subtract 250 from both sides of the equation to get:\r<BR>\n" );
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document.write( "440 - 250 = 50T - 40T\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "190 = 10T\r<BR>\n" );
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document.write( "divide both sides of the equation by 10 to get:\r<BR>\n" );
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document.write( "T = 19\r<BR>\n" );
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document.write( "Solve for D in the first equation to get:\r<BR>\n" );
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document.write( "40(T+11) = D becomes 40(19+11) = D becomes 40(30) = D becomes 1200 = D\r<BR>\n" );
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document.write( "you get D = 1200\r<BR>\n" );
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document.write( "replace T with 19 and D with 1200 in the second equation to get:\r<BR>\n" );
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document.write( "50(T+5) = D becomes 50(19+5) = 1200 becomes 50(24) = 1200 becomes 1200 = 1200.\r<BR>\n" );
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document.write( "this confirms the solution is good for both equations.\r<BR>\n" );
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document.write( "T = 19 and D = 1200.\r<BR>\n" );
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document.write( "you are not asked to find T but you found it in the process of finding D.\r<BR>\n" );
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document.write( "the solution is that the distance to be covered by the trains is 1200 kilometers.\r<BR>\n" );
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document.write( "you could also have solved more directly for T as follows:\r<BR>\n" );
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document.write( "start with:\r<BR>\n" );
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document.write( "40(T+11) = D<BR>\n" );
document.write( "50(T+5) = D\r<BR>\n" );
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document.write( "solve both of these equations for T to get:\r<BR>\n" );
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document.write( "T = (D - 440) / 40 and T = (D - 250) / 50\r<BR>\n" );
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document.write( "set these expressions equal to each other because they are both equal to T and you get:\r<BR>\n" );
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document.write( "(D - 440) / 40 = (D - 250) / 50\r<BR>\n" );
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document.write( "multiply both sides of this equation by 200 to get:\r<BR>\n" );
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document.write( "50 * (D - 440) = 40 * (D - 250)\r<BR>\n" );
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document.write( "simplify both sides of this equation to get:\r<BR>\n" );
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document.write( "50D - 50(440) = 40D - 40(250)\r<BR>\n" );
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document.write( "subtract 40D from both sides of this equation and add 50(440) to both sides of this equation to get:\r<BR>\n" );
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document.write( "50D - 40D = 50(440) - 40(250)\r<BR>\n" );
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document.write( "simplify to get 10D = 12000\r<BR>\n" );
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document.write( "divide both sides of this equation by 10 to get:\r<BR>\n" );
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document.write( "D = 1200 kilometers.\r<BR>\n" );
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document.write( "same answer only you didn't have to find the value of T first in order to get it.\r<BR>\n" );
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document.write( "Either way gets you the answer you are looking for which is that the distance each train has to cover is 1200 kilometers. </SPAN>\n" );
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