document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=2588>Question 2588</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mary left home at 12 noon and drove to visit her mom who lives 20 miles away.  After she arrived she stayed for 2 hours.  Afterwards she drove to her friend Sue's house who lives 15 miles from her mom.  She arrived at Sue's at 3 oclock.  If her speed heading for Sue's was 5 miles per hour faster than her speed going to her mom's, find her average speed on her way to Sue's. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #1123 by </B><A HREF=/tutors/aboutme.mpl?userid=kiru_khandelwal><B>kiru_khandelwal(79)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kiru_khandelwal><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=1123\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the speed with which mary goes to her mom place be x<BR>\n" );
document.write( "So the speed with which mary goes to her freinds place will be x+5\r<BR>\n" );
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document.write( "Mary starts from her home at 12 noon and finally reaches her freinds place at 3'o clock....so total time take by mary is 3 hrs. This 3 hrs also include the time which mary stayed at her mom's place...which is 2 hrs\r<BR>\n" );
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document.write( "Now we know that\r<BR>\n" );
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document.write( "Time = distance/speed\r<BR>\n" );
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document.write( "so time taken by mary to gor from her house to her mom's house will be 20/x<BR>\n" );
document.write( "time taken to go from mom's house to friends house will be 15/(x+5)\r<BR>\n" );
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document.write( "so total time taken is<BR>\n" );
document.write( "20/x + 2 + 15/(x+5)\r<BR>\n" );
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document.write( "But total time taken is 3 hrs\r<BR>\n" );
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document.write( "so the equation will be\r<BR>\n" );
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document.write( "20/x + 2 + 15/(x+5) = 3<BR>\n" );
document.write( "=> 20/x + 15/(x+5) = 1<BR>\n" );
document.write( "=> (20x + 100 + 15x)/x(x+5) = 1<BR>\n" );
document.write( "=> 35x + 100 = x(x+5)<BR>\n" );
document.write( "=> 35x + 100 = x^2 + 5x<BR>\n" );
document.write( "=> x^2 + 5x - 35x -100 = 0<BR>\n" );
document.write( "=> x^2 -30x - 100 = 0<BR>\n" );
document.write( "=> x = 15 +/-5*sqrt(13)<BR>\n" );
document.write( "=> So the speed x will be 15 + 5*sqrt(13). It cant be the other one because speed cannot be negative.\r<BR>\n" );
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document.write( "So her speed to her mom's house is 15 + 5*sqrt(13)<BR>\n" );
document.write( "and speed to sue's house will be 15 + 5*sqrt(13) + 5 = 20 + 5*sqrt(13) </SPAN>\n" );
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