document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=553429>Question 553429</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello tutor, i need help with this problem: (may you please show some steps?)<BR>\n" );
document.write( "Two trains leave Sacramemto at the same time. One travel East at 40mph. The other traveled West at 60mph.Write amd solve a system of linear equations that can be used to determine when the trains are 280 miles apart.\r<BR>\n" );
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document.write( "Thank You!!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #360839 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=360839\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x equals the distance traveled by the first train.<BR>\n" );
document.write( "y equals the distance traveled by the second train.<BR>\n" );
document.write( "the general equation is rate * time = distance.<BR>\n" );
document.write( "you have a series of equations.<BR>\n" );
document.write( "first equation is:<BR>\n" );
document.write( "x + y = 280<BR>\n" );
document.write( "second equation is:<BR>\n" );
document.write( "40z = x<BR>\n" );
document.write( "third equation is:<BR>\n" );
document.write( "60z = y<BR>\n" );
document.write( "z is equal to the time which needs to be the same for both trains because they will be 280 miles apart at the exact same time.<BR>\n" );
document.write( "your 3 equations are:<BR>\n" );
document.write( "x + y = 280<BR>\n" );
document.write( "40z = x<BR>\n" );
document.write( "60z = y<BR>\n" );
document.write( "if you look at these 3 equations, you can see that you can replace x and y in the first equation with 40z and 60z from the second and third equations because they are equivalent.<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "40z + 60z = 280<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "100z = 280<BR>\n" );
document.write( "divide both sides of the equation by 100 to get:<BR>\n" );
document.write( "z = 2.8<BR>\n" );
document.write( "this says that the trains should be 280 miles apart in 2.8 hours.<BR>\n" );
document.write( "let's see if that's true.<BR>\n" );
document.write( "the first train travels 2.8 hours at 40 miles per hour for a distance of 2.8 * 40 = 112 miles.<BR>\n" );
document.write( "the second train travels 2.8 hours at 60 miles per hour for a distance of 2.8 * 60 = 168 miles.<BR>\n" );
document.write( "if you add 112 and 168 you get a total of 280 miles.<BR>\n" );
document.write( "it works out ok and the answer is 2.8 hours.<BR>\n" );
document.write( "in this particular case, we used the process of substitution to narrow down the unknown variable from 3 to 1 and we were left with one equation in one unknown that could be solved.<BR>\n" );
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