document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=832098>Question 832098</A>: <I><SPAN STYLE=\"word-break: break-all;\"> one car travels 300 miles in the same amount of time it takes a second car traveling 5 miles per hour slower than the first to go 275 miles. what are the speeds of the two cars </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #501840 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</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=501840\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What if you are not given specific number values?<BR>\n" );
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document.write( "One car travels d miles in the same amount of time it takes a second car traveling k miles per hour slower than the first to go e miles. what are the speeds of the two cars?\r<BR>\n" );
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document.write( "What are you given?<BR>\n" );
document.write( "Fast Car<BR>\n" );
document.write( "d = 300 miles<BR>\n" );
document.write( "r = speed for fast car<BR>\n" );
document.write( "Slow Car<BR>\n" );
document.write( "e = 275 miles<BR>\n" );
document.write( "k = how much slower is the slower car, a \"miles per hour less\" number<BR>\n" );
document.write( "r -k = speed for slow car<BR>\n" );
document.write( "Both Cars<BR>\n" );
document.write( "t, amount of time is equal for both cars.<BR>\n" );
document.write( "UNKNOWNS: r and t.<BR>\n" );
document.write( "KNOWNS: d, e, k.\r<BR>\n" );
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document.write( "WHICH CAR__________speed____________time___________distance<BR>\n" );
document.write( "FAST_______________r________________t_______________d<BR>\n" );
document.write( "SLOW______________r-k_______________t______________e\r<BR>\n" );
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document.write( "The question is to find r, but the question does not ask for t.  Not really any trouble about t, because it will be equal for both cars.\r<BR>\n" );
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document.write( "We still make some use of t.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%2AT=D ALIGN=MIDDLE  ALT=\"R%2AT=D\"   DISABLED_style= \"max-width:90%; height:auto;\" > for rate, time, distance, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T=D%2FR ALIGN=MIDDLE  ALT=\"T=D%2FR\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Fast Car equation, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=d%2Fr ALIGN=MIDDLE  ALT=\"t=d%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Slow Car equation, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=e%2F%28r-k%29 ALIGN=MIDDLE  ALT=\"t=e%2F%28r-k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The two expressions for t are equal.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28d%2Fr=e%2F%28r-k%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28d%2Fr=e%2F%28r-k%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And because reciprocals will also be equal,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2Fd=%28r-k%29%2Fe ALIGN=MIDDLE  ALT=\"r%2Fd=%28r-k%29%2Fe\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both members by the common denominator of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Ae ALIGN=MIDDLE  ALT=\"d%2Ae\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=re=%28r-k%29d ALIGN=MIDDLE  ALT=\"re=%28r-k%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=re=dr-dk ALIGN=MIDDLE  ALT=\"re=dr-dk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=re-dr=-dk ALIGN=MIDDLE  ALT=\"re-dr=-dk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=er-dr=-dk ALIGN=MIDDLE  ALT=\"er-dr=-dk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28e-d%29=-dk ALIGN=MIDDLE  ALT=\"r%28e-d%29=-dk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both members by negative 1,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28d-e%29=dk ALIGN=MIDDLE  ALT=\"r%28d-e%29=dk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r=%28dk%29%2F%28d-e%29%29 ALIGN=MIDDLE  ALT=\"highlight%28r=%28dk%29%2F%28d-e%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "THAT is a formula for r, the FAST car.  <BR>\n" );
document.write( "Return to the list of variables, substitute their values, and compute r.\r<BR>\n" );
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document.write( "Within sensible reason, you can use this solution and formulas for any general situation fitting the form for the description, no matter (almost) the values for fast or slow vehicles or what is moving in that equal amount of time.  You could choose different variables if you want. </SPAN>\n" );
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