document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117181>Question 117181</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose Sashac, a champion bicyclist, wants to see how far he can travel in an hour. He stats timing himself when he reaches a speed of 45 miles/hour. He maintains this speed for 10 minutes. Sascha starts to feel tired and slows down to 30 m/h for the next 5 minutes. He then reduces his speed to 25 m/h for the next 30 minutes. Finally, Sascha feels exhausted as he finishes the last 15 minutes at 15 m / h. I get the average speed he travels is 28.75 but get that he travels only 26.25 and if he travels for an hour it doesn't make sense what did I do wrong. Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85231 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=85231\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm not sure that I understand your last sentence, but I get a different value for his average speed.<BR>\n" );
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document.write( "Use the formula that Distance = Rate times Time<BR>\n" );
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document.write( "Or in equation form this is<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+R%2AT ALIGN=MIDDLE  ALT=\"D+=+R%2AT\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The units must be consistent ... D is in miles, R in miles per hour, and T in hours.<BR>\n" );
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document.write( "Apply this equation three times ... once for each speed.<BR>\n" );
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document.write( "The first application is for the Rate of 45 miles per hour. The Time at this speed is 10 minutes<BR>\n" );
document.write( "which is (1/6) of an hour. Substitute these values into the equation and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+45%2A%281%2F6%29+=+45%2F6+=+7.5 ALIGN=MIDDLE  ALT=\"D+=+45%2A%281%2F6%29+=+45%2F6+=+7.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So at 45 miles per hour, the distance he travels in ten minutes is 7.5 miles.<BR>\n" );
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document.write( "Use the same process when his speed is 30 miles per hour. He travels at that speed for 5 minutes<BR>\n" );
document.write( "which is (1/12) of an hour. Substitute these values into the equation and the result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+30%2A%281%2F12%29+=+30%2F12+=+2.5 ALIGN=MIDDLE  ALT=\"D+=+30%2A%281%2F12%29+=+30%2F12+=+2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So at 30 miles per hour, the distance he travels in 5 minutes is 2.5 miles.<BR>\n" );
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document.write( "Finally, at the speed of 15 miles per hour, for 15 minutes (or 1/4 hour) the distance he<BR>\n" );
document.write( "travels is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+15%2A%281%2F4%29+=+15%2F4+=+3.75 ALIGN=MIDDLE  ALT=\"D+=+15%2A%281%2F4%29+=+15%2F4+=+3.75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And at 30 miles per hour, the distance he travels in 15 minutes is 3.75 miles.<BR>\n" );
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document.write( "Adding up the the distances you get the total distance traveled is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.5+%2B+2.5+%2B+3.75+=+13.75 ALIGN=MIDDLE  ALT=\"7.5+%2B+2.5+%2B+3.75+=+13.75\"   DISABLED_style= \"max-width:90%; height:auto;\" > miles<BR>\n" );
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document.write( "And the total time it takes to travel that distance is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+%2B+5+%2B+15+=+30 ALIGN=MIDDLE  ALT=\"10+%2B+5+%2B+15+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" > minutes = 1/2 hour<BR>\n" );
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document.write( "The average speed is the total distance (13.75 miles) divided by the time (1/2 hour) which<BR>\n" );
document.write( "results in an average speed of:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Speed+=+13.75%2F%281%2F2%29+=+13.75+%2A+2+=+27.5+ ALIGN=MIDDLE  ALT=\"Speed+=+13.75%2F%281%2F2%29+=+13.75+%2A+2+=+27.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > miles per hour<BR>\n" );
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document.write( "He covered 13.75 miles in the first 30 minutes. If he rides for the next half hour at an<BR>\n" );
document.write( "average speed of 27.5 miles per hour, he will cover 13.75 miles in the second half hour.<BR>\n" );
document.write( "So the total distance he will travel is 13.75 miles + 13.75 miles = 27.5 miles, the same distance<BR>\n" );
document.write( "he would cover if he just rode at a constant speed of 27.5 miles per hour for 1 hour.<BR>\n" );
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document.write( "Does this answer your question? If not, please repost your problem and maybe some other<BR>\n" );
document.write( "tutor will see something that I don't in this problem.<BR>\n" );
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