document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=91645>Question 91645</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the speed of an airplane in still air is 153 mph. The plane travels 849 mph against the wind and 1402 mph with the wind in a total time of 16 hours. what is the speed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #66593 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=66593\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I ASSUME THAT YOU ARE LOOKING FOR THE SPEED OF THE WIND<BR>\n" );
document.write( "Let x=speed of the wind\r<BR>\n" );
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document.write( "distance(d)=rate(r) times time(t) or d=rt; r=d/t and t=d/r\r<BR>\n" );
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document.write( "rate against the wind =153-x<BR>\n" );
document.write( "amount of time the plane travels against the wind=849/(153-x) <BR>\n" );
document.write( "rate with the wind=153+x<BR>\n" );
document.write( "amount of time the plane travels with the wind=1402/(153+x) \r<BR>\n" );
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document.write( "Now we know that the amount of time the plane travels with the wind plus the amount of time the plane travels against the wind=16 hrs.  So our equation to solve is:\r<BR>\n" );
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document.write( "1402/(153+x)+849/(153-x)=16  multiply each term by (153+x)(153-x) to get rid of fractions\r<BR>\n" );
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document.write( "1402(153-x)+849(153+x)=16(153+x)(153-x)  get rid of parens\r<BR>\n" );
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document.write( "214506-1402x+129897+849x=374544-16x^2  add 16x^2 and subtract 374544 from both sides\r<BR>\n" );
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document.write( "214506-374544+16x^2-1402x+129897+849x=374544-374544+16x^2-16x^2 collect like terms\r<BR>\n" );
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document.write( "16x^2-553x-30141=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=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;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28553+%2B-+sqrt%28+%28-553%29%5E2-4%2A16%2A%28-30141%29+%29%29%2F%282%2A16%29+ ALIGN=MIDDLE  ALT=\"x+=+%28553+%2B-+sqrt%28+%28-553%29%5E2-4%2A16%2A%28-30141%29+%29%29%2F%282%2A16%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28553+%2B-+sqrt%28+%28+2234833%29%29%2F%2832%29%29+ ALIGN=MIDDLE  ALT=\"x+=+%28553+%2B-+sqrt%28+%28+2234833%29%29%2F%2832%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28553+%2B-+1494.94%29%2F%2832%29%29+ ALIGN=MIDDLE  ALT=\"x+=+%28553+%2B-+1494.94%29%2F%2832%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28553+%2B+1494.94%29%2F%2832%29%29+ ALIGN=MIDDLE  ALT=\"x+=+%28553+%2B+1494.94%29%2F%2832%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=63.998=+64 ALIGN=MIDDLE  ALT=\"x=63.998=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" > mph----------------------------speed of wind<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28553+-+1494.94%29%2F%2832%29%29+ ALIGN=MIDDLE  ALT=\"x+=+%28553+-+1494.94%29%2F%2832%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > discount negative value for speed of wind\r<BR>\n" );
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document.write( "CK \r<BR>\n" );
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document.write( "1402/(153+64)+849/(153-64)=16 <BR>\n" );
document.write( "1402/217+ 849/89=16<BR>\n" );
document.write( "6.46+9.54=16<BR>\n" );
document.write( "15.9993~~~~~~16   Hope this helps----ptaylor\r<BR>\n" );
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document.write( " </SPAN>\n" );
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