document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=657689>Question 657689</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two planes make a 1000 mile flight, one flying 75 miles per hour faster than the other.  The quicker plane makes the trip 3 hours faster. How long did it take the slower plane to complete the flight? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #410331 by </B><A HREF=/tutors/aboutme.mpl?userid=kevwill><B>kevwill(135)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kevwill><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=kevwill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=410331\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let s be the speed of the slower plane and s+75 be the speed of the faster plane.  \r<BR>\n" );
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document.write( "The time it takes the slower plane to make the flight is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000%2Fs ALIGN=MIDDLE  ALT=\"1000%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The time it takes the faster plane to make the flight is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000%2F%28s%2B75%29 ALIGN=MIDDLE  ALT=\"1000%2F%28s%2B75%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The difference in these two times is 3 hours, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000%2Fs+-+1000%2F%28s%2B75%29+=+3 ALIGN=MIDDLE  ALT=\"1000%2Fs+-+1000%2F%28s%2B75%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28s%2B75%29%2F%28s%2B75%29%29%2A%281000%2Fs%29+-+%28s%2Fs%29%2A%281000%2F%28s%2B75%29%29+=+3 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=%281000%2As%2B75000%29%2F%28s%5E2%2B75%2As%29+-+%281000%2As%29%2F%28s%5E2%2B75%2As%29+=+3 ALIGN=MIDDLE  ALT=\"%281000%2As%2B75000%29%2F%28s%5E2%2B75%2As%29+-+%281000%2As%29%2F%28s%5E2%2B75%2As%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281000%2As+%2B+75000+-+1000%2As%29%2F%28s%5E2+%2B+75%2As%29+=+3 ALIGN=MIDDLE  ALT=\"%281000%2As+%2B+75000+-+1000%2As%29%2F%28s%5E2+%2B+75%2As%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75000%2F%28s%5E2+%2B+75%2As%29+=+3 ALIGN=MIDDLE  ALT=\"75000%2F%28s%5E2+%2B+75%2As%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28s%5E2+%2B+75%2As%29%2A%2875000%2F%28s%5E2+%2B+75%2As%29%29+=+%28s%5E2+%2B+75%2As%29%2A3 ALIGN=MIDDLE  ALT=\"%28s%5E2+%2B+75%2As%29%2A%2875000%2F%28s%5E2+%2B+75%2As%29%29+=+%28s%5E2+%2B+75%2As%29%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75000+=+3%2As%5E2+%2B+225%2As ALIGN=MIDDLE  ALT=\"75000+=+3%2As%5E2+%2B+225%2As\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25000+=+s%5E2+%2B+75%2As ALIGN=MIDDLE  ALT=\"25000+=+s%5E2+%2B+75%2As\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2+%2B+75s+-+25000+=+0 ALIGN=MIDDLE  ALT=\"s%5E2+%2B+75s+-+25000+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We can solve for s using the quadratic equation <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;\" > with a=1, b=75, and c=-25000<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%28-75+%2B-+sqrt%28+75%5E2-4%2A1%2A%28-25000%29+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"s+=+%28-75+%2B-+sqrt%28+75%5E2-4%2A1%2A%28-25000%29+%29%29%2F%282%2A1%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+=+%28-75+%2B-+sqrt%28+5625%2B100000+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"s+=+%28-75+%2B-+sqrt%28+5625%2B100000+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%28-75+%2B-+sqrt%28+105625+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"s+=+%28-75+%2B-+sqrt%28+105625+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%28-75+%2B-+325%29%2F2+ ALIGN=MIDDLE  ALT=\"s+=+%28-75+%2B-+325%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So s = -200 or s = 125.  We'll ignore the negative answer because the planes are not flying backward.<BR>\n" );
document.write( "So the slower plane is flying at 125 mph and completes the trip in 8 hours.<BR>\n" );
document.write( "The faster plane is flying at 200 mph and completes the trip in 5 hours.<BR>\n" );
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