document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=129878>Question 129878</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Airplane A travels 2800 km at a certain speed. Airplane B travels 2000 km at a  speed 50 km/hr faster than plane A and in 3 hours less time. What is the traveling speed of each plane? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #94852 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=94852\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Distance(d) equals Rate(r) times Time(t) or d=rt;r=d/t and t=d/r\r<BR>\n" );
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document.write( "Let r=speed of plane A<BR>\n" );
document.write( "Then r+50=speed of plane B\r<BR>\n" );
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document.write( "Time for plane A=d/r=2800/r<BR>\n" );
document.write( "Time for plane B=d/r=2000/(r+50)\r<BR>\n" );
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document.write( "Now we are told that the travelling time for plane B is three hours less than the travelling time for plane A, so our equation to solve is:\r<BR>\n" );
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document.write( "2000/(r+50)=(2800/r)-3  multiply each term by r(r+50)\r<BR>\n" );
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document.write( "2000r=2800(r+50)-3r(r+50)  get rid of parens\r<BR>\n" );
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document.write( "2000r=2800r+140000-3r^2-150r   subtract 2000r from each side\r<BR>\n" );
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document.write( "2000r-2000r=2800r-2000r+140000-3r^2-150r collect like terms\r<BR>\n" );
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document.write( "0=650r+140000-3r^2  multiply each term by -1\r<BR>\n" );
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document.write( "3r^2-650r-140000=0  quadratic in standard form  solve using the quadratic formula\r<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" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28650+%2B-+sqrt%28+422500%2B4%2A3%2A140000+%29%29%2F%282%2A3%29+ ALIGN=MIDDLE  ALT=\"r+=+%28650+%2B-+sqrt%28+422500%2B4%2A3%2A140000+%29%29%2F%282%2A3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28650+%2B-+sqrt%28+2102500+%29%29%2F%286%29+ ALIGN=MIDDLE  ALT=\"r+=+%28650+%2B-+sqrt%28+2102500+%29%29%2F%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28650+%2B-1450%29%2F%286%29+ ALIGN=MIDDLE  ALT=\"r+=+%28650+%2B-1450%29%2F%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Disregard the negative value for r; rates are positive in this case<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28650+%2B1450%29%2F%286%29+ ALIGN=MIDDLE  ALT=\"r+=+%28650+%2B1450%29%2F%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%282100%29%2F%286%29+ ALIGN=MIDDLE  ALT=\"r+=+%282100%29%2F%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+350+ ALIGN=MIDDLE  ALT=\"r+=+350+\"   DISABLED_style= \"max-width:90%; height:auto;\" > km/hr-------------------speed of plane A\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2B50=350%2B50=400 ALIGN=MIDDLE  ALT=\"r%2B50=350%2B50=400\"   DISABLED_style= \"max-width:90%; height:auto;\" >km/hr--------------------speed of plane B\r<BR>\n" );
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document.write( "CK\r<BR>\n" );
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document.write( "Time for plane A=2800/350=8 hr<BR>\n" );
document.write( "Time for plane B=2000/400=5 hr<BR>\n" );
document.write( "8-5=3<BR>\n" );
document.write( "3=3\r<BR>\n" );
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document.write( "Hope this helps---ptaylor\r<BR>\n" );
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document.write( " </SPAN>\n" );
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