document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=88835>Question 88835</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with this word problem:\r<BR>\n" );
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document.write( "A plane flies 720 miles against a steady 30mi/h head wind and then returns to the same point with the wind. If the entire trip takes 10h, what is the planes speed in still air?\r<BR>\n" );
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document.write( "Thank you for the help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #64597 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=64597\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=rt ALIGN=MIDDLE  ALT=\"d=rt\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the blank rate equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720=%28x%2B30%29%2At%5B1%5D ALIGN=MIDDLE  ALT=\"720=%28x%2B30%29%2At%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now plug in the given values. This is the rate equation <b>with</b> the wind.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720%2F%28x%2B30%29=t%5B1%5D ALIGN=MIDDLE  ALT=\"720%2F%28x%2B30%29=t%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve for t\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720=%28x-30%29%2At%5B2%5D ALIGN=MIDDLE  ALT=\"720=%28x-30%29%2At%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now plug in the given values. This is the rate equation <b>against</b> the wind.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720%2F%28x-30%29=t%5B2%5D ALIGN=MIDDLE  ALT=\"720%2F%28x-30%29=t%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve for t\r<BR>\n" );
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document.write( "Now combine the two \"t\" equations and set them equal to 10\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D%2Bt%5B2%5D=10 ALIGN=MIDDLE  ALT=\"t%5B1%5D%2Bt%5B2%5D=10\"   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=720%2F%28x%2B30%29%2B720%2F%28x-30%29=10 ALIGN=MIDDLE  ALT=\"720%2F%28x%2B30%29%2B720%2F%28x-30%29=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D=720%2F%28x%2B30%29 ALIGN=MIDDLE  ALT=\"t%5B1%5D=720%2F%28x%2B30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B2%5D=720%2F%28x-30%29 ALIGN=MIDDLE  ALT=\"t%5B2%5D=720%2F%28x-30%29\"   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=%28x%2B30%29%28x-30%29%28720%2F%28x%2B30%29%2B720%2F%28x-30%29%29=10%28x%2B30%29%28x-30%29 ALIGN=MIDDLE  ALT=\"%28x%2B30%29%28x-30%29%28720%2F%28x%2B30%29%2B720%2F%28x-30%29%29=10%28x%2B30%29%28x-30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B30%29%28x-30%29 ALIGN=MIDDLE  ALT=\"%28x%2B30%29%28x-30%29\"   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=720%28x-30%29%2B720%28x%2B30%29=10%28x%2B30%29%28x-30%29 ALIGN=MIDDLE  ALT=\"720%28x-30%29%2B720%28x%2B30%29=10%28x%2B30%29%28x-30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720%28x-30%29%2B720%28x%2B30%29=10%28x%5E2-900%29 ALIGN=MIDDLE  ALT=\"720%28x-30%29%2B720%28x%2B30%29=10%28x%5E2-900%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Foil the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720%28x-30%29%2B720%28x%2B30%29=10x%5E2-9000 ALIGN=MIDDLE  ALT=\"720%28x-30%29%2B720%28x%2B30%29=10x%5E2-9000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720x-21600%2B720%28x%2B30%29=10x%5E2-9000 ALIGN=MIDDLE  ALT=\"720x-21600%2B720%28x%2B30%29=10x%5E2-9000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720%28x-30%29 ALIGN=MIDDLE  ALT=\"720%28x-30%29\"   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=720x-21600%2B720x%2B21600=10x%5E2-9000 ALIGN=MIDDLE  ALT=\"720x-21600%2B720x%2B21600=10x%5E2-9000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720%28x%2B30%29 ALIGN=MIDDLE  ALT=\"720%28x%2B30%29\"   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=1440x=10x%5E2-9000 ALIGN=MIDDLE  ALT=\"1440x=10x%5E2-9000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=10x%5E2-1440x-9000 ALIGN=MIDDLE  ALT=\"0=10x%5E2-1440x-9000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 1440x from both sides\r<BR>\n" );
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document.write( "Now let's use the quadratic formula to solve for x:\r<BR>\n" );
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document.write( "Starting with the general quadratic\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the general solution using the quadratic equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Ax%5E2-1440%2Ax-9000=0 ALIGN=MIDDLE  ALT=\"10%2Ax%5E2-1440%2Ax-9000=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=10 ALIGN=MIDDLE  ALT=\"a=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-1440 ALIGN=MIDDLE  ALT=\"b=-1440\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-9000 ALIGN=MIDDLE  ALT=\"c=-9000\"   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=x+=+%28--1440+%2B-+sqrt%28+%28-1440%29%5E2-4%2A10%2A-9000+%29%29%2F%282%2A10%29 ALIGN=MIDDLE  ALT=\"x+=+%28--1440+%2B-+sqrt%28+%28-1440%29%5E2-4%2A10%2A-9000+%29%29%2F%282%2A10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=10, b=-1440, and c=-9000\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281440+%2B-+sqrt%28+%28-1440%29%5E2-4%2A10%2A-9000+%29%29%2F%282%2A10%29 ALIGN=MIDDLE  ALT=\"x+=+%281440+%2B-+sqrt%28+%28-1440%29%5E2-4%2A10%2A-9000+%29%29%2F%282%2A10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -1440 to get 1440\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281440+%2B-+sqrt%28+2073600-4%2A10%2A-9000+%29%29%2F%282%2A10%29 ALIGN=MIDDLE  ALT=\"x+=+%281440+%2B-+sqrt%28+2073600-4%2A10%2A-9000+%29%29%2F%282%2A10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -1440 to get 2073600\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281440+%2B-+sqrt%28+2073600%2B360000+%29%29%2F%282%2A10%29 ALIGN=MIDDLE  ALT=\"x+=+%281440+%2B-+sqrt%28+2073600%2B360000+%29%29%2F%282%2A10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-9000%2A10 ALIGN=MIDDLE  ALT=\"-4%2A-9000%2A10\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360000 ALIGN=MIDDLE  ALT=\"360000\"   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=x+=+%281440+%2B-+sqrt%28+2433600+%29%29%2F%282%2A10%29 ALIGN=MIDDLE  ALT=\"x+=+%281440+%2B-+sqrt%28+2433600+%29%29%2F%282%2A10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281440+%2B-+1560%29%2F%282%2A10%29 ALIGN=MIDDLE  ALT=\"x+=+%281440+%2B-+1560%29%2F%282%2A10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281440+%2B-+1560%29%2F20 ALIGN=MIDDLE  ALT=\"x+=+%281440+%2B-+1560%29%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 10 to get 20\r<BR>\n" );
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document.write( "So now the expression breaks down into two parts\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281440+%2B+1560%29%2F20 ALIGN=MIDDLE  ALT=\"x+=+%281440+%2B+1560%29%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281440+-+1560%29%2F20 ALIGN=MIDDLE  ALT=\"x+=+%281440+-+1560%29%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Lets look at the first part:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%281440+%2B+1560%29%2F20 ALIGN=MIDDLE  ALT=\"x=%281440+%2B+1560%29%2F20\"   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=x=3000%2F20 ALIGN=MIDDLE  ALT=\"x=3000%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add the terms in the numerator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=150 ALIGN=MIDDLE  ALT=\"x=150\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So one answer is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=150 ALIGN=MIDDLE  ALT=\"x=150\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now lets look at the second part:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%281440+-+1560%29%2F20 ALIGN=MIDDLE  ALT=\"x=%281440+-+1560%29%2F20\"   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=x=-120%2F20 ALIGN=MIDDLE  ALT=\"x=-120%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract the terms in the numerator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6 ALIGN=MIDDLE  ALT=\"x=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So another answer is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6 ALIGN=MIDDLE  ALT=\"x=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our solutions are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=150 ALIGN=MIDDLE  ALT=\"x=150\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6 ALIGN=MIDDLE  ALT=\"x=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since a negative speed doesn't make any sense, our solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=150 ALIGN=MIDDLE  ALT=\"x=150\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the plane's speed in still air is 150 mph </SPAN>\n" );
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