document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204036>Question 1204036</A>: <I><SPAN STYLE=\"word-break: break-all;\"> steve McPoke left home on his bivcycle at 8 am. traveling at 18 km/h. at 10 am, steve's brother set out after him on a motorcycle , folowing the same route. The motorcycle traveled at 54 km/h. How long had steve traveled when his brother overtok him? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840037 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=840037\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Let's start with the distance formula:<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;\" > where <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 traveled, <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 (speed), and <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 of travel.  \r<BR>\n" );
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document.write( "We can write two such equations, one for Steve (1) and the other for his brother (2):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D+=+r%5B1%5D%2At%5B1%5D ALIGN=MIDDLE  ALT=\"d%5B1%5D+=+r%5B1%5D%2At%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >......eq. (1) <BR>\n" );
document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D+=+r%5B2%5D%2At%5B2%5D ALIGN=MIDDLE  ALT=\"d%5B2%5D+=+r%5B2%5D%2At%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......eq.(2)\r<BR>\n" );
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document.write( "Now when Steve's brother on the motor bike overtakes Steve on his bicycle, each will have traveled the same distance, so:\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D+=+d%5B2%5D ALIGN=MIDDLE  ALT=\"d%5B1%5D+=+d%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "and, since Steve's brother set out two hours after Steve did (10 am - 8 am), then Steve's time is two hours more than his brother's time, and, of course, the speeds of both are given, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D+=+t%5B2%5D%2B2 ALIGN=MIDDLE  ALT=\"t%5B1%5D+=+t%5B2%5D%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now we have enough information to complete the two equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+18%2A%28t%5B2%5D%2B2%29 ALIGN=MIDDLE  ALT=\"d+=+18%2A%28t%5B2%5D%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+54%2A%28t%5B2%5D%29 ALIGN=MIDDLE  ALT=\"d+=+54%2A%28t%5B2%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+d ALIGN=MIDDLE  ALT=\"d+=+d\"   DISABLED_style= \"max-width:90%; height:auto;\" > we'll set these two equations equal to each other to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2A%28t%5B2%5D%2B2%29+=+54%2At%5B2%5D ALIGN=MIDDLE  ALT=\"18%2A%28t%5B2%5D%2B2%29+=+54%2At%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >........ Solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B2%5D ALIGN=MIDDLE  ALT=\"t%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2At%5B2%5D%2B36+=+54%2At%5B2%5D ALIGN=MIDDLE  ALT=\"18%2At%5B2%5D%2B36+=+54%2At%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >......... Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2At%5B2%5D ALIGN=MIDDLE  ALT=\"18%2At%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36+=+36%2At%5B2%5D ALIGN=MIDDLE  ALT=\"36+=+36%2At%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > ........Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36 ALIGN=MIDDLE  ALT=\"36\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B2%5D+=+1 ALIGN=MIDDLE  ALT=\"t%5B2%5D+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > but we want Steve's time (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D ALIGN=MIDDLE  ALT=\"t%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D+=+t%5B2%5D%2B2 ALIGN=MIDDLE  ALT=\"t%5B1%5D+=+t%5B2%5D%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >....... Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B2%5D+=+1 ALIGN=MIDDLE  ALT=\"t%5B2%5D+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D+=+1%2B2 ALIGN=MIDDLE  ALT=\"t%5B1%5D+=+1%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28t%5B1%5D+=+3%29 ALIGN=MIDDLE  ALT=\"highlight%28t%5B1%5D+=+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Steve had traveled for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours when his brother overtook him.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );