document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=121967>Question 121967</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0130442631/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> a mortocycle breaks down and the rider has to walk the rest of the way to work.  The motorcycle was traveling at 45 mi/h, and the rider walks at a speed of 6 mi/h.  The distance from home to work is 25miles, and the total time for the trip was 2 hours.  How far did the motorcycle go before it broke down? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #89545 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=89545\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let T represent the time in hours that the rider uses the motorcycle. Then, since the total <BR>\n" );
document.write( "time for the trip was 2 hours, the time spent walking is 2 hours less the time on the motorcycle<BR>\n" );
document.write( "... or 2 - T hours spent walking.<BR>\n" );
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document.write( "Next use the fact that distance traveled is equal to the rate of travel multiplied by the amount<BR>\n" );
document.write( "of time that passes for the type of transportation having that rate. <BR>\n" );
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document.write( "Since the motorcycle has a rate of 45 mi/h and the amount of time that the rider uses the<BR>\n" );
document.write( "motorcycle is T hours, the distance covered on the motorcycle is 45 * T miles or 45T.<BR>\n" );
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document.write( "And similarly, the rider walks at 6 mi/h and the time spent walking is 2 - T hrs, the distance<BR>\n" );
document.write( "covered by walking is 6*(2 - T) = 12 - 6T.<BR>\n" );
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document.write( "So the total miles covered is the sum of these two distances or:<BR>\n" );
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document.write( "45T + 12 - 6T<BR>\n" );
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document.write( "Combine the 45T and the -6T and this expression of the total distance reduces to:<BR>\n" );
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document.write( "39T + 12<BR>\n" );
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document.write( "The problem tells you that the total distance is 25 miles ... so you can set the two total<BR>\n" );
document.write( "distances equal to get:<BR>\n" );
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document.write( "39T + 12 = 25<BR>\n" );
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document.write( "Get rid of the 12 on the left side by subtracting 12 from both sides to get:<BR>\n" );
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document.write( "39T = 13<BR>\n" );
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document.write( "Solve for T by dividing both sides by 39 and you get:<BR>\n" );
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document.write( "T = 13/39 = 1/3 hours<BR>\n" );
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document.write( "But earlier we said that the distance covered by the motorcycle which travels at 45 mi/h is<BR>\n" );
document.write( "45 times T. So we can say that the distance covered by the motorcycle is:<BR>\n" );
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document.write( "D = 45*T = 45*(1/3) = 45/3 = 15 miles<BR>\n" );
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document.write( "So the motorcycle breaks down after covering 15 miles.<BR>\n" );
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document.write( "Check. Since 1/3 of an hour is spent on the motorcycle, the remainder of the 2 hours is<BR>\n" );
document.write( "spent walking. And 2 hours is equal to 6/3 hours. Take 1/3 hour away from the 6/3 hours<BR>\n" );
document.write( "and you find that 5/3 hours is spent walking. At the rate of 6 mi/h the distance covered<BR>\n" );
document.write( "walking is:<BR>\n" );
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document.write( "Distance = 6 * 5/3 = 30/3 = 10 miles<BR>\n" );
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document.write( "So the rider covers 15 miles on the motorcycle and 10 miles walking for the total of 25<BR>\n" );
document.write( "miles. Everything checks out. <BR>\n" );
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document.write( "This means that our answer of 15 miles on the motorcycle is correct.<BR>\n" );
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document.write( "Hope this helps you to see how you can work your way through this problem.<BR>\n" );
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