document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=183141>Question 183141</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a university flew its football team round trip for a game with a rival uiversty. the distance was 520 miles each way, and the round trip required a total flying time of 8.8 hours. because of wind, the average speed of the plane in one directon was 30 miles per hour faster than it was in the opposite direction.what would be the speed of the plane in still air? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #137651 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=137651\">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 s=speed of plane in still air<BR>\n" );
document.write( "And let r=speed of the wind<BR>\n" );
document.write( "s+r=plane speed with the wind <BR>\n" );
document.write( "s-r=plane speed against the wind.  We are told that:<BR>\n" );
document.write( "s+r=(s-r)+30  subtract s from and add r to each side<BR>\n" );
document.write( "2r=30<BR>\n" );
document.write( "r=15 mph speed of wind<BR>\n" );
document.write( "time against the wind=520/(s-15)<BR>\n" );
document.write( "time with the wind=520/(s+15)<BR>\n" );
document.write( "And we are told that time with wind + time against wind =8.8 hr, so:<BR>\n" );
document.write( "520/(s-15) + 520/(s+15)=8.8  multiply each term by (s-15)(s+15)<BR>\n" );
document.write( "520(s+15)+520(s-15)=8.8(s-15)(s+15) get rid of parens<BR>\n" );
document.write( "520s+7800+520s-7800=8.8s^2-1980 simplify<BR>\n" );
document.write( "1040s-8.8s^2+1980=0 or<BR>\n" );
document.write( "8.8s^2-1040s-1980=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=s+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"s+=+%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=s+=+%281040+%2B-+sqrt%28+%281040%29%5E2-4%2A%288.8%29%2A%28-1980%29+%29%29%2F%282%2A%288.8%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%281040+%2B-+sqrt%281081600%2B69696+%29%29%2F%2817.6%29 ALIGN=MIDDLE  ALT=\"s+=+%281040+%2B-+sqrt%281081600%2B69696+%29%29%2F%2817.6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%281040+%2B-+sqrt%28+1151296%29%29%2F%2817.6%29 ALIGN=MIDDLE  ALT=\"s+=+%281040+%2B-+sqrt%28+1151296%29%29%2F%2817.6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%281040+%2B-+%281072.98%29%29%2F%2817.6%29 ALIGN=MIDDLE  ALT=\"s+=+%281040+%2B-+%281072.98%29%29%2F%2817.6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Disregard negative value for s, speed is positive<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%281040+%2B%281072.98%29%29%2F%2817.6%29 ALIGN=MIDDLE  ALT=\"s+=+%281040+%2B%281072.98%29%29%2F%2817.6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+120.1 ALIGN=MIDDLE  ALT=\"s+=+120.1\"   DISABLED_style= \"max-width:90%; height:auto;\" >mph---------------------speed of plane in still air\r<BR>\n" );
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document.write( "CK<BR>\n" );
document.write( "520/(120.1+15) +520/(120.1-15)=8.8<BR>\n" );
document.write( "3.849+4.95=8.8<BR>\n" );
document.write( "~~~~8.8=8.8\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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