document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=164547>Question 164547</A>: <I><SPAN STYLE=\"word-break: break-all;\"> First tourist walked a distance of 30 km in a time 10 minutes shorter than the second tourist. Calculate their speeds if the speed of the first one was 3 km/h greater than that of the second one. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121286 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=121286\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First tourist walked a distance of 30 km in a time 10 minutes shorter than the second tourist. Calculate their speeds if the speed of the first one was 3 km/h greater than that of the second one.\r<BR>\n" );
document.write( "\n" );
document.write( "Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r\r<BR>\n" );
document.write( "\n" );
document.write( "Since the problem is dealing in both hours and minutes, we'll just keep it simple and deal in hours<BR>\n" );
document.write( "Let t=time it took second tourist to walk 30km<BR>\n" );
document.write( "Then t-(1/6)=time it took first tourist to walk 30 km<BR>\n" );
document.write( "Rate (speed) of second tourist=30/t<BR>\n" );
document.write( "Rate of first tourist=30/(t-(1/6)) and we are told that this is 3 km/hr greater than the speed of the second tourist, so our equation to solve is\r<BR>\n" );
document.write( "\n" );
document.write( "(30/(t-(1/6)))-3=30/t  multiply each term by t(t-(1/6))<BR>\n" );
document.write( "30t-3t(t-(1/6))=30(t-(1/6))  get rid of parens (distributive law)\r<BR>\n" );
document.write( "\n" );
document.write( "30t-3t^2+0.5t=30t-5 subtract 30t from and also add 5 to both sides<BR>\n" );
document.write( "30t-30t-3t^2+0.5t+5=30t-30t-5+5  collect like terms<BR>\n" );
document.write( "-3t^2+0.5t+5=0   multiply each term by -1<BR>\n" );
document.write( "3t^2-0.5t-5=0 Quadratic in standard form; solve using the quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%280.5+%2B-+sqrt%28+0.25-4%2A3%2A%28-5%29+%29%29%2F%286%29+ ALIGN=MIDDLE  ALT=\"t+=+%280.5+%2B-+sqrt%28+0.25-4%2A3%2A%28-5%29+%29%29%2F%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%280.5+%2B-+sqrt%2860.25%29%29%2F%286%29+ ALIGN=MIDDLE  ALT=\"t+=+%280.5+%2B-+sqrt%2860.25%29%29%2F%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%280.5+%2B-7.76%29%2F%286%29+ ALIGN=MIDDLE  ALT=\"t+=+%280.5+%2B-7.76%29%2F%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%280.5+%2B7.76%29%2F%286%29+ ALIGN=MIDDLE  ALT=\"t+=+%280.5+%2B7.76%29%2F%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%288.26%29%2F%286%29+ ALIGN=MIDDLE  ALT=\"t+=+%288.26%29%2F%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+1.377 ALIGN=MIDDLE  ALT=\"t+=+1.377\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs----time it took second tourist<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t-%281%2F6%29=t-0.167=1.377-0.677=1.21 ALIGN=MIDDLE  ALT=\"t-%281%2F6%29=t-0.167=1.377-0.677=1.21\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs-----time it took first tourist<BR>\n" );
document.write( "rate of second tourist=30/1.377=21.8 km/hr--------------------ans<BR>\n" );
document.write( "rate of first tourist=30/1.21=24.8 km/hr------------------------ans\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%280.5+-7.76%29%2F%286%29+ ALIGN=MIDDLE  ALT=\"t+=+%280.5+-7.76%29%2F%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > --------------disregard the negative value for t\r<BR>\n" );
document.write( "\n" );
document.write( "Hope this helps----ptaylor<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );