document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=350906>Question 350906</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A driver makes a 125 mile trip from Phoenix to Tucson with the cruise control set at either 55 mph or 75 mph the whole way. If the trip took 1.8 hours, how long did the driver travel at 55 mph?\r<BR>\n" );
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document.write( "if i had an equation to solve this problem, i can solve similar problems. I was thinking along the lines of 55x+ 75y= 1.8?? iknow it has something to do with the slope formula....but i dont know how. Ive been working on this and similar problems for over an hour, and  cant seem to figure how to solve it. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #250823 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=250823\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> he is either traveling at 75 mph or 55 mph the whole way.\r<BR>\n" );
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document.write( "total time it took for the trip is 1.8 hours.\r<BR>\n" );
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document.write( "total distance is 125 miles.\r<BR>\n" );
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document.write( "rate * time = distance is the general formula to apply to this type of problem.\r<BR>\n" );
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document.write( "let x = the time it takes to travel at 55 miles per hour.\r<BR>\n" );
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document.write( "let y = the time it takes to travel at 75 miles per hour.\r<BR>\n" );
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document.write( "we get:\r<BR>\n" );
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document.write( "55*x + 75*y = 125\r<BR>\n" );
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document.write( "55*x is the distance traveled in x hours at 55 miles per hour.\r<BR>\n" );
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document.write( "75*y is the distance traveled in y hours at 75 miles per hour.\r<BR>\n" );
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document.write( "total distance is 125 miles.\r<BR>\n" );
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document.write( "we also get:\r<BR>\n" );
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document.write( "x + y = 1.8 since the total time is 1.8 hours.\r<BR>\n" );
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document.write( "x is the time it takes to travel at 55 miles per hour.\r<BR>\n" );
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document.write( "y is the time it takes to travel at 75 miles per hour.\r<BR>\n" );
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document.write( "we solve these 2 equations simultaneously and we get our answer.\r<BR>\n" );
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document.write( "from x + y = 1.8 we can solve for y to get y = 1.8 - x\r<BR>\n" );
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document.write( "we substitute for y in the equation of:\r<BR>\n" );
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document.write( "55*x + 75*y = 125 to get:\r<BR>\n" );
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document.write( "55*x + 75*(1.8-x) = 125\r<BR>\n" );
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document.write( "Simplify to get:\r<BR>\n" );
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document.write( "55*x + 75*1.8 - 75*x = 125\r<BR>\n" );
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document.write( "combine like terms and simplify further to get:\r<BR>\n" );
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document.write( "-20*x + 135 = 125\r<BR>\n" );
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document.write( "subtract 135 from both sides to get:\r<BR>\n" );
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document.write( "-20*x = -10\r<BR>\n" );
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document.write( "divide both sides by -20 to get:\r<BR>\n" );
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document.write( "x = 1/2 = .5\r<BR>\n" );
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document.write( "this makes y = 1.8 - .5 = 1.3\r<BR>\n" );
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document.write( "looks like .5 hours at 55 mph and 1.3 hours at 75 mph.\r<BR>\n" );
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document.write( "55 * .5 + 75 * 1.3 = 27.5 + 97.5 = 125 so the numbers look good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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