document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1153814>Question 1153814</A>: <I><SPAN STYLE=\"word-break: break-all;\"> \"A truck driver traveled at an average speed of 56 miles per hour on a 200-mile<BR>\n" );
document.write( "trip to pick up a load of freight. On the return trip (with the truck fully<BR>\n" );
document.write( "loaded), the average speed was 37 miles per hour. Find the average speed for the<BR>\n" );
document.write( "round trip.\"\r<BR>\n" );
document.write( "\n" );
document.write( "That is the question, and the answer is 44.6mi/hr.<BR>\n" );
document.write( "But I don't know how to get to that answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #776130 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=776130\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Two responses you have received at this point have shown finding the average speed as total distance divided by total time:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=total+distance%2Ftotal+time+=+400%2F%28%28200%2F56%29%2B200%2F37%29%29 ALIGN=MIDDLE  ALT=\"total+distance%2Ftotal+time+=+400%2F%28%28200%2F56%29%2B200%2F37%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That is an ugly kind of calculation that I prefer to avoid.<br><BR>\n" );
document.write( "This is how I would solve the problem.<br><BR>\n" );
document.write( "The ratio of speeds is 56:37; since the distances are the same, the ratio of times is 37:56.<br><BR>\n" );
document.write( "That means the truck driver travels at 56mph for 37/(56+37) of the time and at 37mph for 56/(56+37) of the time.  The average speed is then the WEIGHTED average<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2837%2F%2856%2B37%29%29%2A56%2B%2856%2F%2856%2B37%29%29%2A37+=+%282%2A37%2A56%29%2F%2856%2B37%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > = 44.56 to 2 decimal places<br><BR>\n" );
document.write( "That to me is an easier calculation for finding the answer.<br><BR>\n" );
document.write( "Note that that calculation is exactly what the other tutor @ikleyn shows in her response: for a round trip at two different speeds, the average speed is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%28v%281%29%29%28v%282%29%29%29%2F%28v%281%29%2Bv%282%29%29 ALIGN=MIDDLE  ALT=\"%282%28v%281%29%29%28v%282%29%29%29%2F%28v%281%29%2Bv%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Note that one reason this calculation is easier is that it does not use the given distance.  The average speed is independent of the distance -- a point tutor @ikleyn also makes in her response.<br><BR>\n" );
document.write( "So if you were (or are) in a situation where you need to do this kind of calculation frequently, the easiest thing to do is memorize the formula and use it....<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );