document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=125482>Question 125482</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Either I missed something or the plane has lost distance.\r<BR>\n" );
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document.write( "A plane climbs into the jet stream which is flowing at a rate of 80 miles per hour. It travels with the jet stream for 5 hours and then reduces its altitude, flying out of the jet stream for 4 more hours. The plane, while out of the jet stream, covered 550 miles less than it did during the 5 hours it was in the jet stream. How fast was the plane flying out of the jet stream? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #91932 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=91932\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the distance = rate times time formula, <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;\" >\r<BR>\n" );
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document.write( "Since we are trying to find the rate for the plane out of the jet stream, let that rate be r.  Then we know that the rate while in the jet stream must be r + 80.\r<BR>\n" );
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document.write( "The distance traveled while in the jet stream, d, must be equal to the rate while in the jet stream times the 5 hours that it flew in the jet stream, or:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=5%28r%2B80%29 ALIGN=MIDDLE  ALT=\"d=5%28r%2B80%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The distance traveled while out of the jet stream is 550 miles less than the distance traveled in the jet stream, so we can express that distance as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d-550 ALIGN=MIDDLE  ALT=\"d-550\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but we can also express this distance as r, the rate out of the jet stream times 4, the number of hours flown out of the jet stream, or:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d-550=4r ALIGN=MIDDLE  ALT=\"d-550=4r\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Re-writing the first equation we get:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=5r%2B400 ALIGN=MIDDLE  ALT=\"d=5r%2B400\"   DISABLED_style= \"max-width:90%; height:auto;\" >, giving us an expression for d that can be substituted into the second equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5r%2B400-550=4r ALIGN=MIDDLE  ALT=\"5r%2B400-550=4r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5r-150=4r ALIGN=MIDDLE  ALT=\"5r-150=4r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5r-4r=150 ALIGN=MIDDLE  ALT=\"5r-4r=150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=150 ALIGN=MIDDLE  ALT=\"r=150\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the speed of the aircraft out of the jet stream.\r<BR>\n" );
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document.write( "Check the answer.\r<BR>\n" );
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document.write( "If the speed out of the jet stream is 150, then the speed in the jet stream must be 230.  230 times 5 = 1150, so the airplane traveled 1150 miles while in the jet stream.\r<BR>\n" );
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document.write( "The speed out of the jet stream is 150, so the distance traveled out of the jet stream is 150 times 4 = 600, and 600 = 1150 - 550.  Answer checks.\r<BR>\n" );
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