document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1036035>Question 1036035</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Thaddeus and Ian start at the same location and drive in opposite directions, but leave at different times. When they are 270 miles apart, their combined travel time is 8 hours.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #650611 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=650611\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rate * time = distance.\r<BR>\n" );
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document.write( "let a be the time it takes thaddeus.<BR>\n" );
document.write( "let 8 - a be the time it takes ian.<BR>\n" );
document.write( "let c be the distance that thaddeus travels.<BR>\n" );
document.write( "let 270 - c be the distance that ian travels.\r<BR>\n" );
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document.write( "the rate * time formula for thaddeus becomes 30 * a = c<BR>\n" );
document.write( "the rate * time formula for ian becomes 35 * (8 - a) = (270 - c)\r<BR>\n" );
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document.write( "their combined formula becomes:\r<BR>\n" );
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document.write( "30 * a + 35 * (8 - a) = c + (270 - c)\r<BR>\n" );
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document.write( "simplify this formula to get:\r<BR>\n" );
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document.write( "30 * a + 35 * 8 - 35 * a = c + 270 - c\r<BR>\n" );
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document.write( "simplify further and combine like terms to get:\r<BR>\n" );
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document.write( "-5 * a + 280 = 270\r<BR>\n" );
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document.write( "subtract 280 from both sides of this formula to get:\r<BR>\n" );
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document.write( "-5 * a = -10\r<BR>\n" );
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document.write( "divide both sides of this formula to get:\r<BR>\n" );
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document.write( "a = 2\r<BR>\n" );
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document.write( "since a = 2, then 8 - a must be equal to 6.\r<BR>\n" );
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document.write( "the formula for thaddeus becomes 30 * 2 = c<BR>\n" );
document.write( "the formula for ian becomes 35 * 6 = 270 - c\r<BR>\n" );
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document.write( "in the first formula, solve for c to get c = 60.<BR>\n" );
document.write( "in the second formula, solve for 270 - c to get 270 - c = 210.\r<BR>\n" );
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document.write( "the formulas become:\r<BR>\n" );
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document.write( "30 * 2 = 60<BR>\n" );
document.write( "35 * 6 = 210\r<BR>\n" );
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document.write( "thaddeus traveled 60 miles in 2 hours.<BR>\n" );
document.write( "ian traveled 210 miles in 6 hours.\r<BR>\n" );
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document.write( "you were asked how long each was driving.\r<BR>\n" );
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document.write( "thaddeus was driving for 2 hours and ian was driving for 6 hours.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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