document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=111421>Question 111421</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321319095/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Could you please help me with an application question involving a quadratic equation?<BR>\n" );
document.write( "The question is: On a sales trip, Gail drives the 600 mi to Richmond at a certain speed.  The return trip is made at a speed that is 10 mph slower.  Total time for the round trip is 22 hr.  How fast did Gail travel on each part of the trip?\r<BR>\n" );
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document.write( "This is what I've got so far:<BR>\n" );
document.write( "t[1]=600/r<BR>\n" );
document.write( "t[2]=600/(r-10)<BR>\n" );
document.write( "(600/r)+(600/(r-10))=22<BR>\n" );
document.write( "r(r-10)(600/r)+r(r-10)(600/(r-10))=r(r-10)22<BR>\n" );
document.write( "600(r-10)+600r=22r(r-10)<BR>\n" );
document.write( "600r-6000+600r=22r^2-220r<BR>\n" );
document.write( "22r^2-1420r+6000=0<BR>\n" );
document.write( "I know at this point to plug it into quadratic equation form... but when factoring this I get decimal numbers, so it seems wrong.<BR>\n" );
document.write( "-(-64.545)+-(sqrt(-64.545)^2-4(1)(272.727))/2(1)<BR>\n" );
document.write( "64.545+-(sqrt4166.057-1090.908)/2<BR>\n" );
document.write( "64.545+-(sqrt3075.149)/2<BR>\n" );
document.write( "(64.545+55.454)/2=60<BR>\n" );
document.write( "or<BR>\n" );
document.write( "(64.545-55.454)/2=4.5<BR>\n" );
document.write( "Please help!<BR>\n" );
document.write( "Thank you in advance for your help!<BR>\n" );
document.write( "Brenda </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #81253 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=81253\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Everything is great until you reach the point where you factor out the leading coefficient (which you don't need to do). So I'm going to start off with the step that has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22r%5E2-1420r%2B6000=0 ALIGN=MIDDLE  ALT=\"22r%5E2-1420r%2B6000=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic_formula.solver>Quadratic Formula</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Let's use the quadratic formula to solve for r:<BR><BR>\n" );
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document.write( "  Starting with the general quadratic<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ar%5E2%2Bbr%2Bc=0 ALIGN=MIDDLE  ALT=\"ar%5E2%2Bbr%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  the general solution using the quadratic equation is:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"r+=+%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" );
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document.write( "  So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22%2Ar%5E2-1420%2Ar%2B6000=0 ALIGN=MIDDLE  ALT=\"22%2Ar%5E2-1420%2Ar%2B6000=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=22 ALIGN=MIDDLE  ALT=\"a=22\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-1420 ALIGN=MIDDLE  ALT=\"b=-1420\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=6000 ALIGN=MIDDLE  ALT=\"c=6000\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28--1420+%2B-+sqrt%28+%28-1420%29%5E2-4%2A22%2A6000+%29%29%2F%282%2A22%29 ALIGN=MIDDLE  ALT=\"r+=+%28--1420+%2B-+sqrt%28+%28-1420%29%5E2-4%2A22%2A6000+%29%29%2F%282%2A22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=22, b=-1420, and c=6000<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%281420+%2B-+sqrt%28+%28-1420%29%5E2-4%2A22%2A6000+%29%29%2F%282%2A22%29 ALIGN=MIDDLE  ALT=\"r+=+%281420+%2B-+sqrt%28+%28-1420%29%5E2-4%2A22%2A6000+%29%29%2F%282%2A22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -1420 to get 1420<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%281420+%2B-+sqrt%28+2016400-4%2A22%2A6000+%29%29%2F%282%2A22%29 ALIGN=MIDDLE  ALT=\"r+=+%281420+%2B-+sqrt%28+2016400-4%2A22%2A6000+%29%29%2F%282%2A22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -1420 to get 2016400  (note: remember when you square -1420, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1420%29%5E2=-1420%2A-1420=2016400 ALIGN=MIDDLE  ALT=\"%28-1420%29%5E2=-1420%2A-1420=2016400\"   DISABLED_style= \"max-width:90%; height:auto;\" >.)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%281420+%2B-+sqrt%28+2016400%2B-528000+%29%29%2F%282%2A22%29 ALIGN=MIDDLE  ALT=\"r+=+%281420+%2B-+sqrt%28+2016400%2B-528000+%29%29%2F%282%2A22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A6000%2A22 ALIGN=MIDDLE  ALT=\"-4%2A6000%2A22\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-528000 ALIGN=MIDDLE  ALT=\"-528000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%281420+%2B-+sqrt%28+1488400+%29%29%2F%282%2A22%29 ALIGN=MIDDLE  ALT=\"r+=+%281420+%2B-+sqrt%28+1488400+%29%29%2F%282%2A22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%281420+%2B-+1220%29%2F%282%2A22%29 ALIGN=MIDDLE  ALT=\"r+=+%281420+%2B-+1220%29%2F%282%2A22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%281420+%2B-+1220%29%2F44 ALIGN=MIDDLE  ALT=\"r+=+%281420+%2B-+1220%29%2F44\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 22 to get 44<BR>\n" );
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document.write( "  So now the expression breaks down into two parts<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%281420+%2B+1220%29%2F44 ALIGN=MIDDLE  ALT=\"r+=+%281420+%2B+1220%29%2F44\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%281420+-+1220%29%2F44 ALIGN=MIDDLE  ALT=\"r+=+%281420+-+1220%29%2F44\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Lets look at the first part:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%281420+%2B+1220%29%2F44 ALIGN=MIDDLE  ALT=\"x=%281420+%2B+1220%29%2F44\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=2640%2F44 ALIGN=MIDDLE  ALT=\"r=2640%2F44\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add the terms in the numerator<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=60 ALIGN=MIDDLE  ALT=\"r=60\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide<BR>\n" );
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document.write( "  So one answer is<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=60 ALIGN=MIDDLE  ALT=\"r=60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Now lets look at the second part:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%281420+-+1220%29%2F44 ALIGN=MIDDLE  ALT=\"x=%281420+-+1220%29%2F44\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=200%2F44 ALIGN=MIDDLE  ALT=\"r=200%2F44\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract the terms in the numerator<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=50%2F11 ALIGN=MIDDLE  ALT=\"r=50%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide<BR>\n" );
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document.write( "  So another answer is<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=50%2F11 ALIGN=MIDDLE  ALT=\"r=50%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  So our solutions are:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=60 ALIGN=MIDDLE  ALT=\"r=60\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=50%2F11 ALIGN=MIDDLE  ALT=\"r=50%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "note: ignore the graph. It didn't turn out the way I wanted it to.\r<BR>\n" );
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document.write( "Now notice that we get two answers. However if we subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50%2F11-10 ALIGN=MIDDLE  ALT=\"50%2F11-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > (or 5.45-10) we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50%2F11-10=-50%2F11 ALIGN=MIDDLE  ALT=\"50%2F11-10=-50%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is a negative number. So we must discard the second solution.\r<BR>\n" );
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document.write( "So her original speed was 60 mph and her slower speed was 50 mph </SPAN>\n" );
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