document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=249444>Question 249444</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mrs. Smith drove at a rate of 45 mph from her home to her sisters house.  she spent 1.5 hrs having lunch with her sister. She then drove back home at a rate of 55 mph.  The entire trip, including lunch, took 4 hrs.  How far does Mrs. Smith live from her sister?<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 #181676 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=181676\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The elapsed time is 4 hr of which 2.5 hr was driving time.<BR>\n" );
document.write( "The distance formula is d = rt, where d=distance, r=rate, t=time<BR>\n" );
document.write( "We assume the distance to her sister's is the same as it is home (or she drives the same path both ways without any detours).<BR>\n" );
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document.write( "We can define the equation for driving to her sister's house:<BR>\n" );
document.write( "d = 45(t)<BR>\n" );
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document.write( "Then the equation for driving home from her sister's house is:<BR>\n" );
document.write( "d = 55(2.5-t)<BR>\n" );
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document.write( "In this way, we have defined the two unknown times in terms of a single unknown variable 't' and '2.5-t'.<BR>\n" );
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document.write( "Since d = d, we can say:<BR>\n" );
document.write( "45t = 55(2.5-t)<BR>\n" );
document.write( "45t = 137.5 - 55t<BR>\n" );
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document.write( "Adding 55t to both sides<BR>\n" );
document.write( "100t = 137.5<BR>\n" );
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document.write( "Dividing both sides by 100<BR>\n" );
document.write( "t = 1.375<BR>\n" );
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document.write( "So the time spend driving to her sister's house at 45 mph = 1.375 hr<BR>\n" );
document.write( "The time spend driving home at 55 mph = 2.5 - 1.375 =  1.125 hr<BR>\n" );
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document.write( "How far does she travel at 45 mph?<BR>\n" );
document.write( "d = 45 mph * 1.375 hr = 61.875 miles.<BR>\n" );
document.write( "How far does she travel at 55 mph?<BR>\n" );
document.write( "d = 55 mph * 1.125 hr = 61.875 miles.<BR>\n" );
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document.write( "So we've checked our work and are confident the distance is 61.875 = 61 7/8 miles.<BR>\n" );
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document.write( "We could be asked what her average speed was, too.<BR>\n" );
document.write( "Was it simply (45+55)/2?<BR>\n" );
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document.write( "Well, we see that 2d = 2*61.875 = 123.75 miles<BR>\n" );
document.write( "And it took 2.5 hr, so<BR>\n" );
document.write( "t = d/r = 123.75/2.5 = 49.5.<BR>\n" );
document.write( "So her average speed was 49.5.<BR>\n" );
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document.write( "Done. </SPAN>\n" );
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