document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=982361>Question 982361</A>: <I><SPAN STYLE=\"word-break: break-all;\"> On a journey of 100km, Jim travels at a certain speed for the first 60km, and then increases his speed by 15km/h for the remainder. If the whole journey takes 2 hours, find his two speeds.<BR>\n" );
document.write( "I'm in year 10, and this is an A-standard question which neither of my parents nor I could solve. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #603178 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39630)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=603178\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Uniform Rates for Travel, RT=D relates rate, time, distance.\r<BR>\n" );
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document.write( "Let r be the unknown rate for the first part;<BR>\n" );
document.write( "let d be the unknown distance of the second part;\r<BR>\n" );
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document.write( "___________________rate_____________time_____________distance<BR>\n" );
document.write( "part1_______________r_______________(___)_____________60<BR>\n" );
document.write( "part2______________r+15_____________(___)_____________d<BR>\n" );
document.write( "TOTALS_______________________________2________________100\r<BR>\n" );
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document.write( "Form expressions for the missing time quantities from the basic idea <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=RT=D ALIGN=MIDDLE  ALT=\"RT=D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=RT%2FR=D%2FR ALIGN=MIDDLE  ALT=\"RT%2FR=D%2FR\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28T=D%2FR%29 ALIGN=MIDDLE  ALT=\"highlight_green%28T=D%2FR%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "___________________rate_____________time_____________distance<BR>\n" );
document.write( "part1_______________r_______________60/r______________60<BR>\n" );
document.write( "part2______________r+15_____________d/(r+15)___________d<BR>\n" );
document.write( "TOTALS_______________________________2________________100\r<BR>\n" );
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document.write( "Note that the distance sum arrangement will give the unknown part2 distance.<BR>\n" );
document.write( "60+d=100<BR>\n" );
document.write( "d=100-60<BR>\n" );
document.write( "d=40<BR>\n" );
document.write( "and you can adjust the tabulated information:\r<BR>\n" );
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document.write( "___________________rate_____________time_____________distance<BR>\n" );
document.write( "part1_______________r_______________60/r______________60<BR>\n" );
document.write( "part2______________r+15_____________40/(r+15)__________40<BR>\n" );
document.write( "TOTALS_______________________________2________________100\r<BR>\n" );
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document.write( "The total time will give an equation in the single variable, r.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2Fr%2B40%2F%28r%2B15%29=2 ALIGN=MIDDLE  ALT=\"60%2Fr%2B40%2F%28r%2B15%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This can be partly simplified to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2860%2Fr%2B40%2F%28r%2B15%29%29%281%2F2%29=2%281%2F2%29 ALIGN=MIDDLE  ALT=\"%2860%2Fr%2B40%2F%28r%2B15%29%29%281%2F2%29=2%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%2830%2Fr%2B20%2F%28r%2B15%29=1%29 ALIGN=MIDDLE  ALT=\"highlight_green%2830%2Fr%2B20%2F%28r%2B15%29=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Can you solve this equation for r ?\r<BR>\n" );
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document.write( "The algebra steps give a factorable quadratic equation, making the final answer apparent.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28highlight%28r=45%29%29 ALIGN=MIDDLE  ALT=\"highlight%28highlight%28r=45%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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