document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=135>Question 135</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with this word problem.  It seems easy at first, but the answer that I got was denied by my math teacher.  He said it's supposed to be harder than that.   So here it goes:\r<BR>\n" );
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document.write( "A man is traveling up a hill at 30 mph and immediately returns down.  His average speed for the whole trip is 45 mph.  What is the man's speed going down the hill?\r<BR>\n" );
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document.write( "At first, I thought it was 60 mph, but my algebra teacher said it was wrong.  Is it because the word problem does not say how long it took the man to travel up and down the hill?  My algebra teacher said that the question was answerable, so please help me out.  Thank you.\r<BR>\n" );
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document.write( "Katie, 14 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108 by </B><A HREF=/tutors/aboutme.mpl?userid=ichudov><B>ichudov(507)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ichudov><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/cgi-bin/show-face.mpl?user=ichudov><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=108\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The time it took the man to travel uphill is:\r<BR>\n" );
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document.write( "time to travel uphill = distance/30 mph<BR>\n" );
document.write( "time to travel downhill = distance/downhill speed\r<BR>\n" );
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document.write( "Average speed is the total distance (which is twice the distance to go one way), divided by total time:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=average_speed+=+%282%2Adistance%2F%28distance%2F30%2Bdistance%2Fdownhill_speed%29%29+ ALIGN=MIDDLE  ALT=\"average_speed+=+%282%2Adistance%2F%28distance%2F30%2Bdistance%2Fdownhill_speed%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "we know that average_speed is 45:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45+=+%282%2Adistance%2F%28distance%2F30%2Bdistance%2Fdownhill_speed%29%29+ ALIGN=MIDDLE  ALT=\"45+=+%282%2Adistance%2F%28distance%2F30%2Bdistance%2Fdownhill_speed%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplifying\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45=%282%2Adistance%2F%28%28distance%2Adownhill_speed%2Bdistance%2A30%29%2F%2830%2Adownhill_speed%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "distance cancels out (and that's why it was not given in the problem):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45=%282%2F%28%28downhill_speed%2B30%29%2F%2830%2Adownhill_speed%29%29%29+ ALIGN=MIDDLE  ALT=\"45=%282%2F%28%28downhill_speed%2B30%29%2F%2830%2Adownhill_speed%29%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45=%282%2A30%2Adownhill_speed%29%2F%28downhill_speed%2B30%29+ ALIGN=MIDDLE  ALT=\"45=%282%2A30%2Adownhill_speed%29%2F%28downhill_speed%2B30%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%2A%28downhill_speed%2B30%29+=+60%2Adownhill_speed ALIGN=MIDDLE  ALT=\"45%2A%28downhill_speed%2B30%29+=+60%2Adownhill_speed\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "45*downhill_speed+30*45 = 60*downhill_speed<BR>\n" );
document.write( "15*downhill_speed = 30*45<BR>\n" );
document.write( "downhill_speed = 30*3 = 90 </SPAN>\n" );
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