document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=376451>Question 376451</A>: <I><SPAN STYLE=\"word-break: break-all;\"> To deliver a package, a messenger must travel at a speed of 60mi/h on land and then use a motorboat whose speed is 20mi/h in still water. The messenger goes by land to a dock and then travels on a river against a current of 4mi/h. He reaches the destination in 4.5 hours and then returns to the starting point in 3.5 hours. How far did the messenger travel by land and how far by water?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #267892 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=267892\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To deliver a package, a messenger must travel at a speed of 60mi/h on land<BR>\n" );
document.write( " and then use a motorboat whose speed is 20mi/h in still water.<BR>\n" );
document.write( " The messenger goes by land to a dock and then travels on a river against a current of 4mi/h.<BR>\n" );
document.write( " He reaches the destination in 4.5 hours and then returns to the starting point in 3.5 hours.<BR>\n" );
document.write( " How far did the messenger travel by land and how far by water? <BR>\n" );
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document.write( "Let x = distance on land<BR>\n" );
document.write( "Let y = distance on water<BR>\n" );
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document.write( "Write a time equation and simplify, for each trip<BR>\n" );
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document.write( "Land time + water time = total time<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F60 ALIGN=MIDDLE  ALT=\"x%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2F%28%2820-4%29%29 ALIGN=MIDDLE  ALT=\"y%2F%28%2820-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F60 ALIGN=MIDDLE  ALT=\"x%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2F16 ALIGN=MIDDLE  ALT=\"y%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4.5<BR>\n" );
document.write( "Multiply by 60*16 to get rid of the denominators<BR>\n" );
document.write( "16x + 60y = 4.5(960)<BR>\n" );
document.write( "16x + 60y = 4320<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F60 ALIGN=MIDDLE  ALT=\"x%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2F%28%2820%2B4%29%29 ALIGN=MIDDLE  ALT=\"y%2F%28%2820%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F60 ALIGN=MIDDLE  ALT=\"x%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2F24 ALIGN=MIDDLE  ALT=\"y%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3.5<BR>\n" );
document.write( "Multiply by 60*24 to get rid of the denominators<BR>\n" );
document.write( "24x + 60y = 3.5(1440)<BR>\n" );
document.write( "24x + 60y = 5040<BR>\n" );
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document.write( "Use elimination here; subtract 16x + 60y = 4320 from the above equation<BR>\n" );
document.write( "24x + 60y = 5040<BR>\n" );
document.write( "16x + 60y = 4320<BR>\n" );
document.write( "-------------------subtraction eliminates y find x:<BR>\n" );
document.write( "8x = 720<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720%2F8 ALIGN=MIDDLE  ALT=\"720%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 90 miles on land<BR>\n" );
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document.write( "Find y using 16x + 60y = 4320<BR>\n" );
document.write( "16(90) + 60y = 4320<BR>\n" );
document.write( "1440 + 60y = 4320<BR>\n" );
document.write( "60y = 4320 - 1440<BR>\n" );
document.write( "60y = 2880<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2880%2F60 ALIGN=MIDDLE  ALT=\"2880%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = 48 miles by water<BR>\n" );
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document.write( "Check these values in the original 1st equation<BR>\n" );
document.write( "90/60 + 48/16 =<BR>\n" );
document.write( "1.5 + 3 = 4.5, confirms our solutions </SPAN>\n" );
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