document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=646572>Question 646572</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A search plane has a cruising speed of 250 mph and carries enough fuel for at most 5 hours of flying. If there is a wind that averages 30 mph and the direction of the search is with the wind one way and against it the other, how far can the search team travel before it has to turn back? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #405910 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=405910\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A search plane has a cruising speed of 250 mph and carries enough fuel<BR>\n" );
document.write( " for at most 5 hours of flying. <BR>\n" );
document.write( "If there is a wind that averages 30 mph and the direction of the search<BR>\n" );
document.write( " is with the wind one way and against it the other, how far can the search<BR>\n" );
document.write( " team travel before it has to turn back?<BR>\n" );
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document.write( "This is a \"point of no return\" problem<BR>\n" );
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document.write( "Let d = the one-way distance to the point of no return<BR>\n" );
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document.write( "250 - 30 = 220 mph ground speed against the wind<BR>\n" );
document.write( "250 + 30 = 280 mph ground speed with the wind<BR>\n" );
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document.write( "Write a time equation; Time = dist/speed<BR>\n" );
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document.write( "outbound time + inbound time = 5 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F220 ALIGN=MIDDLE  ALT=\"d%2F220\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F280 ALIGN=MIDDLE  ALT=\"d%2F280\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5<BR>\n" );
document.write( "find the least common multiple, prime factor<BR>\n" );
document.write( "22: 2, 11<BR>\n" );
document.write( "28: 2, 2, 7<BR>\n" );
document.write( "2*2*7*11*10 = 3080<BR>\n" );
document.write( "Multiply equation by 3080<BR>\n" );
document.write( "3080*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F220 ALIGN=MIDDLE  ALT=\"d%2F220\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 3080*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F280 ALIGN=MIDDLE  ALT=\"d%2F280\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3080*5<BR>\n" );
document.write( "Cancel the denominators<BR>\n" );
document.write( "14d + 11d = 15400<BR>\n" );
document.write( "d = 15400/25<BR>\n" );
document.write( "d = 616 miles to turn back point<BR>\n" );
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document.write( "Check this by finding the actual time each way<BR>\n" );
document.write( "616/220 = 2.8 hrs outbound<BR>\n" );
document.write( "616/280 = 2.2 hrs to return<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "total time: 5 hrs </SPAN>\n" );
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