document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=653001>Question 653001</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A locomotive travels on a straight track at a constant speed of 40 mi/h, then reverses direction and returns to its starting point, traveling at a constant speed of 60 mi/h. <BR>\n" );
document.write( "What is the average velocity for the round-trip?<BR>\n" );
document.write( "What is the average speed for the round-trip?<BR>\n" );
document.write( "What is the total distance traveled by the train if the total trip took 5 h?\r<BR>\n" );
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document.write( "I have no idea where to even begin... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #408200 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=408200\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Let the direction of travel for the initial leg of the trip be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE X^\circ\">.  Then the direction of travel for the return leg is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(X^\circ\ +\ 180^\circ\right)\ \text{mod}\ 360^\circ\">.  The vector sum of the two opposing vectors is the difference of the magnitudes in the direction of the greater magnitude, i.e. 20 mph @ <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(X^\circ\ +\ 180^\circ\right)\ \text{mod}\ 360^\circ\">.\r<BR>\n" );
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document.write( "The average speed is the total distance traveled divided by the total travel time.  The time for the outward leg is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{d}{40}\ \ \">hours.\r<BR>\n" );
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document.write( "Where the one-way distance is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE d\">\r<BR>\n" );
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document.write( "The time for the return leg is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{d}{60}\ \ \">hours.\r<BR>\n" );
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document.write( "The sum of these times is the total travel time:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{d}{40}\ +\ \frac{d}{60}\ =\ \frac{100d}{2400}\ =\ \frac{d}{24}\ \ \">hours.\r<BR>\n" );
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document.write( "The total distance travelled is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 2d\">, so the average speed is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{2d}{\frac{d}{24}}\ =\ 48\ \ \">mph.\r<BR>\n" );
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document.write( "If the trip took 5 hours...\r<BR>\n" );
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document.write( "If you go 48 mph for 5 hours, how far did you go?\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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