document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=422364>Question 422364</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Maria loves to walk. on Monday, she left her son's house at noon and arrived at her daughter's house 15 minutes later. the next, she left her daughter's house at noon and arrived at her son's house 20 minutes later. both days, she followed exactly the same rout (she did not stop and she did not retrace her steps). how many points along the way did she pass at exactly the some time on both days? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #295195 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=295195\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Maria loves to walk. on Monday, she left her son's house at noon and arrived at her daughter's house 15 minutes later. the next, she left her daughter's house at noon and arrived at her son's house 20 minutes later. both days, she followed exactly the same rout (she did not stop and she did not retrace her steps). how many points along the way did she pass at exactly the some time on both days?\r<BR>\n" );
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document.write( "let d=distance beetween Marie's son's and daughter's houses<BR>\n" );
document.write( "Let x=distance traveled to the point where Marie passed thru during both days in the foward direction.<BR>\n" );
document.write( "d-x=distance traveled to the point where Marie passed thru during both days in the return direction.<BR>\n" );
document.write( "time traveled=distance/speed (the same in both directions of travel)<BR>\n" );
document.write( "d/15=speed from son's to daughter's house<BR>\n" );
document.write( "d/20=speed from daughter,s to son's house<BR>\n" );
document.write( "travel time = distance/speed (same for both directions of travel)<BR>\n" );
document.write( "x/(d/15)=(d-x)/(d/20)<BR>\n" );
document.write( "15x/d=20(d-x)/d<BR>\n" );
document.write( "15x=20d-20x<BR>\n" );
document.write( "35x=20d<BR>\n" );
document.write( "x=(20/35)d=(4/7)d<BR>\n" );
document.write( "This means the distance traveled to the point during the first day is 4/7 of the total distance. It follows this took 4/7 of the total time of the trip.<BR>\n" );
document.write( "=(4/7)*15=60/7 minutes. <BR>\n" );
document.write( "Total time after noon is (4/7)*15=60/7 minutes<BR>\n" );
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document.write( "On the return trip the distance to the same point coming from the other direction is 3/7 of the total distance.<BR>\n" );
document.write( "Total time after noon is also (3/7)*20=60/7 minutes<BR>\n" );
document.write( "ans:<BR>\n" );
document.write( "Marie pass only one point at exactly 60/7 minutes after noon both days?\r<BR>\n" );
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