document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151330>Question 1151330</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Madeline made a certain trip by moped in 2 hours. It took her 2.5 hours to make the return trip, since her average speed returning was 12 km/h less than her speed going. Find Madeline's average speed in each direction.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #773065 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=773065\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Let's say Madeline goes from point A to B and it takes her 2 hours. Her speed is some unknown, which we'll call x km/hr. \r<BR>\n" );
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document.write( "When she goes from B to A, it takes her 2.5 hours and her speed is (x-12) km/hr. <BR>\n" );
document.write( "Both trips travel the same distance (assume she takes the same roads for both trips), which we'll call d.\r<BR>\n" );
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document.write( "Going from A to B<BR>\n" );
document.write( "distance = rate*time<BR>\n" );
document.write( "d = x*2<BR>\n" );
document.write( "d = 2x\r<BR>\n" );
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document.write( "Going from B to A<BR>\n" );
document.write( "distance = rate*time<BR>\n" );
document.write( "d = (x-12)*2.5<BR>\n" );
document.write( "d = 2.5x - 30\r<BR>\n" );
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document.write( "Because 'd' is the same for both equations, we can use substitution and solve for x.<BR>\n" );
document.write( "d = 2.5x - 30<BR>\n" );
document.write( "2x = 2.5x - 30 .... replace d with 2x<BR>\n" );
document.write( "2x-2.5x = -30<BR>\n" );
document.write( "-0.5x = -30<BR>\n" );
document.write( "x = -30/(-0.5)<BR>\n" );
document.write( "x = 60\r<BR>\n" );
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document.write( "Now we know that x = 60, we can say,<BR>\n" );
document.write( "x-12 = 60-12 = 48\r<BR>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "The speed for the 2 hour trip was <font color=red size=4>60 km/hr</font><BR>\n" );
document.write( "The speed for the 2.5 hour trip was <font color=red size=4>48 km/hr</font>\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "If Madeline travels for 2 hours at 60 km/hr, then she covers a distance of<BR>\n" );
document.write( "d = r*t = 60*2 = 120 km<BR>\n" );
document.write( "If Madeline travels for 2.5 hours at 48 km/hr, then she covers a distance of<BR>\n" );
document.write( "d = r*t = 48*2.5 = 120 km<BR>\n" );
document.write( "She covers the same distance both ways, which helps us confirm we have the right answers.<BR>\n" );
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