document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=359168>Question 359168</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The road from Tedium to Excitement is uphill for 5 miles, level for 4 miles, and then downhill for 6 miles. John Mayer walks from Excitement to Tedium in 4 hours. Later he walks halfway from Tedium to Excitement and back again in 3 hours and 55 minutes. Finally he walks all the way to Excitement from Tedium in 3 hours and 52 minutes. What are his rates going uphill, downhill, and on level ground assuming that these rates remain constant? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #256442 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=256442\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The road from Tedium to Excitement is uphill for 5 miles, level for 4 miles,<BR>\n" );
document.write( " and then downhill for 6 miles.<BR>\n" );
document.write( " John Mayer walks from Excitement to Tedium in 4 hours.<BR>\n" );
document.write( " Later he walks halfway from Tedium to Excitement and back again in 3 hours and 55 minutes.<BR>\n" );
document.write( " Finally he walks all the way to Excitement from Tedium in 3 hours and 52 minutes.<BR>\n" );
document.write( " What are his rates going uphill, downhill, and on level ground assuming that<BR>\n" );
document.write( " these rates remain constant?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let u = uphill rate<BR>\n" );
document.write( "Let f = flat rate<BR>\n" );
document.write( "Let d = downhill rate<BR>\n" );
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document.write( "Write a time equation for each statement: Time = dist/rate<BR>\n" );
document.write( "We are going to do it in minutes, change it to hrs later<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"John Mayer walks from Excitement to Tedium in 4 hours.\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Fu ALIGN=MIDDLE  ALT=\"6%2Fu\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ff ALIGN=MIDDLE  ALT=\"4%2Ff\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Fd ALIGN=MIDDLE  ALT=\"5%2Fd\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 240<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"he walks halfway from Tedium to Excitement and back again in 3 hours and 55 min.\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Fu ALIGN=MIDDLE  ALT=\"5%2Fu\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Ff ALIGN=MIDDLE  ALT=\"5%2Ff\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Fd ALIGN=MIDDLE  ALT=\"5%2Fd\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 235 (halfway is 7.5 mi)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"he walks all the way to Excitement from Tedium in 3 hours and 52 minutes.\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Fu ALIGN=MIDDLE  ALT=\"5%2Fu\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ff ALIGN=MIDDLE  ALT=\"4%2Ff\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Fd ALIGN=MIDDLE  ALT=\"6%2Fd\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 232<BR>\n" );
document.write( ":<BR>\n" );
document.write( " What are his rates going uphill, downhill, and on level ground assuming that these rates remain constant?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Use elimination on the 1st and 2nd equations<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Fu ALIGN=MIDDLE  ALT=\"6%2Fu\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ff ALIGN=MIDDLE  ALT=\"4%2Ff\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Fd ALIGN=MIDDLE  ALT=\"5%2Fd\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 240<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Fu ALIGN=MIDDLE  ALT=\"5%2Fu\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Ff ALIGN=MIDDLE  ALT=\"5%2Ff\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Fd ALIGN=MIDDLE  ALT=\"5%2Fd\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 235<BR>\n" );
document.write( "-----------------------------------------Subtraction eliminates d<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fu ALIGN=MIDDLE  ALT=\"1%2Fu\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ff ALIGN=MIDDLE  ALT=\"1%2Ff\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Multiply the 1st equation by 6 and the 3rd equation by 5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2Fu ALIGN=MIDDLE  ALT=\"30%2Fu\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2Ff ALIGN=MIDDLE  ALT=\"30%2Ff\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2Fd ALIGN=MIDDLE  ALT=\"30%2Fd\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1410<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2Fu ALIGN=MIDDLE  ALT=\"25%2Fu\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2Ff ALIGN=MIDDLE  ALT=\"20%2Ff\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2Fd ALIGN=MIDDLE  ALT=\"30%2Fd\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1160<BR>\n" );
document.write( "--------------------------------------------------Subtraction eliminates d again<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Fu ALIGN=MIDDLE  ALT=\"5%2Fu\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Ff ALIGN=MIDDLE  ALT=\"10%2Ff\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 250<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Multiply the 1st 2 unknown equation by 10, add to the above equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Fu ALIGN=MIDDLE  ALT=\"5%2Fu\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Ff ALIGN=MIDDLE  ALT=\"10%2Ff\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 250<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Fu ALIGN=MIDDLE  ALT=\"10%2Fu\"   DISABLED_style= \"max-width:90%; height:auto;\" > -<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Ff ALIGN=MIDDLE  ALT=\"10%2Ff\"   DISABLED_style= \"max-width:90%; height:auto;\" > =  50<BR>\n" );
document.write( "------------------addition eliminates f, find u<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2Fu ALIGN=MIDDLE  ALT=\"15%2Fu\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 300<BR>\n" );
document.write( "u = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F300 ALIGN=MIDDLE  ALT=\"15%2F300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "u = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F20 ALIGN=MIDDLE  ALT=\"1%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" > miles per minute, that's <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F20 ALIGN=MIDDLE  ALT=\"1%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" > * 60 = 3 mph up hill<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Use the equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fu ALIGN=MIDDLE  ALT=\"1%2Fu\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ff ALIGN=MIDDLE  ALT=\"1%2Ff\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5 to find f,(were dealing mi/min here)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%281%2F20%29 ALIGN=MIDDLE  ALT=\"1%2F%281%2F20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ff ALIGN=MIDDLE  ALT=\"1%2Ff\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5<BR>\n" );
document.write( "20 - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ff ALIGN=MIDDLE  ALT=\"1%2Ff\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5<BR>\n" );
document.write( "-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ff ALIGN=MIDDLE  ALT=\"1%2Ff\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5 - 20<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2Ff ALIGN=MIDDLE  ALT=\"-1%2Ff\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -15<BR>\n" );
document.write( "f = +<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F15 ALIGN=MIDDLE  ALT=\"1%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi/min, that's <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F15 ALIGN=MIDDLE  ALT=\"1%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" > * 60 = 4 mph on the flat area<BR>\n" );
document.write( ":<BR>\n" );
document.write( "We can use the 1st equation, using hrs, to find d<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F3 ALIGN=MIDDLE  ALT=\"6%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F4 ALIGN=MIDDLE  ALT=\"4%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Fd ALIGN=MIDDLE  ALT=\"5%2Fd\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4<BR>\n" );
document.write( "2 + 1 + 5/d = 4<BR>\n" );
document.write( "5/d = 4 - 3<BR>\n" );
document.write( "5/d = 1<BR>\n" );
document.write( "d = 5 mph down hill<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Summarize here<BR>\n" );
document.write( "u = 3 mph uphill<BR>\n" );
document.write( "f = 4 mph level<BR>\n" );
document.write( "d = 5 mph down hill<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "See if this works int he original 3rd equation, using hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F3 ALIGN=MIDDLE  ALT=\"5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F4 ALIGN=MIDDLE  ALT=\"4%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F5 ALIGN=MIDDLE  ALT=\"6%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3 hr 52 min<BR>\n" );
document.write( "1.67 + 1 + 1.2 = 3.87 hrs which is 3 hrs, .87*60 = 52.2 min, close enough </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );