document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=341418>Question 341418</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One train runs 90% of the time and goes 55 mph any time it runs (no acceleration time lag). Another train runs 10% of the time. How fast does this train have to go (mph) to exceed the distance of the other train?\r<BR>\n" );
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document.write( "Hint: Examine the speeds of the train for many, many hours to come up with the speed as a whole number. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #244497 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=244497\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One train runs 90% of the time and goes 55 miles per hour.<BR>\n" );
document.write( "The other train runs 10% of the time.\r<BR>\n" );
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document.write( "The total distance that each train will travel is given by D.\r<BR>\n" );
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document.write( "The formula we will work with is R * T = D.\r<BR>\n" );
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document.write( "The first travels 90% of the Time, so the first train will achieve D in .9*T\r<BR>\n" );
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document.write( "The formula for the first train will be R * .9*T = D\r<BR>\n" );
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document.write( "Since R = 55 miles per hour, then the formula for the first train becomes 55 * .9*T = D which becomes 49.5 * T = D.\r<BR>\n" );
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document.write( "The formula for the second train is R * .1*T = D\r<BR>\n" );
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document.write( "We want to find an equation where the distance traveled by the second train exceeds (is greater than) the distance traveled by the first train.\r<BR>\n" );
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document.write( "This means that D for the second train is greater than D for the second train.\r<BR>\n" );
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document.write( "Since for the first train, we know that 49.5 * T = D, and for the second train we know that R * .1 * T = D, then we can assume that:\r<BR>\n" );
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document.write( "49.5 * T = R * .1 * T because they are both equal to the same thing and are therefore equal to each other.\r<BR>\n" );
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document.write( "Since we want the D of second train to be greater than the D of the first train, then we change our equation to read:\r<BR>\n" );
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document.write( "49.5 * T < R * .1 * T.\r<BR>\n" );
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document.write( "If we divide both sides of this equation by T, then we should get:\r<BR>\n" );
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document.write( "49.5 < .1 * R\r<BR>\n" );
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document.write( "If we further divide both sides of this equation by .1, then we should get:\r<BR>\n" );
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document.write( "495 < R\r<BR>\n" );
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document.write( "It appears that the second train must travel at a rate greater than 495 miles per hour in order to exceed the distance traveled by the first train.\r<BR>\n" );
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document.write( "Let's see if that holds true.\r<BR>\n" );
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document.write( "Assume the first train travels at 55 miles per hour.<BR>\n" );
document.write( "Assume the second train travels at 495 miles per hour.\r<BR>\n" );
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document.write( "Assume the total time is 10 hours.\r<BR>\n" );
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document.write( "This means that the first train is traveling for 9 hours and the second train is traveling 1 hour.\r<BR>\n" );
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document.write( "9 * 55 = 495\r<BR>\n" );
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document.write( "1 * 495 = 495\r<BR>\n" );
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document.write( "They travel the same distance.\r<BR>\n" );
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document.write( "Now assume the second train travels at a speed greater than 495 miles per hour.\r<BR>\n" );
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document.write( "Assume the second train is traveling at 500 miles per hour.\r<BR>\n" );
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document.write( "9 * 55 is still 495.\r<BR>\n" );
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document.write( "1 * 500 is 500 which is greater than 495.\r<BR>\n" );
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document.write( "The answer looks good.\r<BR>\n" );
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