document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173469>Question 173469</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Carlos leaves LA on a cross country car trip at 8 AM, he is going 50 mph; Juanita plans to do the same but leaves at 9 AM and travels 60 mph, develop a diagram or table to determine at what time Juanita will pass Carlos </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #128345 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=128345\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For both of them, <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;\" >, where<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" >= distance<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >= rate<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" >= time<BR>\n" );
document.write( "So, for Carlos,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bc%5D+=+r%5Bc%5D%2At%5Bc%5D ALIGN=MIDDLE  ALT=\"d%5Bc%5D+=+r%5Bc%5D%2At%5Bc%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And for Juanita,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bj%5D+=+r%5Bj%5D%2At%5Bj%5D ALIGN=MIDDLE  ALT=\"d%5Bj%5D+=+r%5Bj%5D%2At%5Bj%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "The chart would look like this:<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "Distances  --  rates  --  times<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( " -- d[c] --  -- r[c] -- -- t[c]<BR>\n" );
document.write( " -- d[j] --  -- r[j] -- -- t[j]<BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "Now I can repace some of these variables<BR>\n" );
document.write( "with things that I know about them<BR>\n" );
document.write( "For instance, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bc%5D+=+d%5Bj%5D ALIGN=MIDDLE  ALT=\"d%5Bc%5D+=+d%5Bj%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > because <BR>\n" );
document.write( "the distance is from LA to the place<BR>\n" );
document.write( "where they meet. I'll call them both <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "Distances  --  rates  --  times<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( " -- d --  -- r[c] --  -- t[c]<BR>\n" );
document.write( " -- d --  -- r[j] --  -- t[j]<BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "Carlos travels 50 mi/hr and Juanita travels 60 mi/hr, so<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "Distances  --  rates  --  times<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( " -- d --  -- 50 --     -- t[c]<BR>\n" );
document.write( " -- d --  -- 60 --     -- t[j]<BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "Juanita leaves LA an hour later, so she has to cover the same <BR>\n" );
document.write( "distance in 1 hour less time, so<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "Distances  --  rates  --  times<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( " -- d --    -- 50 --    --t[c]<BR>\n" );
document.write( " -- d --    -- 60 --    --t[c] - 1<BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "Now I can use this to find out when Juanita will pass Carlos.<BR>\n" );
document.write( "The problem doesn't ask for it, but I'll do the algebra<BR>\n" );
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;\" > for both of them, so<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+50t%5Bc%5D ALIGN=MIDDLE  ALT=\"d+=+50t%5Bc%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+60%2A%28t%5Bc%5D+-+1%29 ALIGN=MIDDLE  ALT=\"d+=+60%2A%28t%5Bc%5D+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+60t%5Bc%5D+-+60 ALIGN=MIDDLE  ALT=\"d+=+60t%5Bc%5D+-+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" >s are the same in (1) and (2), <BR>\n" );
document.write( "so I'll set them equal to eachother<BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50t%5Bc%5D+=+60t%5Bc%5D+-+60 ALIGN=MIDDLE  ALT=\"50t%5Bc%5D+=+60t%5Bc%5D+-+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10t%5Bc%5D+=+60 ALIGN=MIDDLE  ALT=\"10t%5Bc%5D+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bc%5D+=+6 ALIGN=MIDDLE  ALT=\"t%5Bc%5D+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And, since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bj%5D+=+t%5Bc%5D+-+1 ALIGN=MIDDLE  ALT=\"t%5Bj%5D+=+t%5Bc%5D+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bj%5D+=+6+-+1 ALIGN=MIDDLE  ALT=\"t%5Bj%5D+=+6+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bj%5D+=+5 ALIGN=MIDDLE  ALT=\"t%5Bj%5D+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Carlos left LA at 8AM, so 6 hours later, <BR>\n" );
document.write( "it would have been 2PM<BR>\n" );
document.write( "Juanita left LA at 9AM, so 5 hours later,<BR>\n" );
document.write( "It would have been 2PM, which is when she passed him<BR>\n" );
document.write( "check answer:<BR>\n" );
document.write( "The distances must be the same, so<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+50t%5Bc%5D ALIGN=MIDDLE  ALT=\"d+=+50t%5Bc%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+50%2A6 ALIGN=MIDDLE  ALT=\"d+=+50%2A6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+300 ALIGN=MIDDLE  ALT=\"d+=+300\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+60t%5Bc%5D+-+60 ALIGN=MIDDLE  ALT=\"d+=+60t%5Bc%5D+-+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+60%2A6+-+60 ALIGN=MIDDLE  ALT=\"d+=+60%2A6+-+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+360+-+60 ALIGN=MIDDLE  ALT=\"d+=+360+-+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+300 ALIGN=MIDDLE  ALT=\"d+=+300\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi<BR>\n" );
document.write( "OK </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );