document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=287285>Question 287285</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Plane 1 can travel 1400 miles in 1 hour less time than it tales plane B to travel 2000 miles. The rate of plane B is 50 miles per hour greater than the rate of plane A. Find the times and rates of both planes. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #208243 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=208243\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Plane 1 can travel 1400 miles in 1 hour less time than it tales plane B to travel 2000 miles. <BR>\n" );
document.write( "The rate of plane B is 50 miles per hour greater than the rate of plane A.<BR>\n" );
document.write( " Find the times and rates of both planes.<BR>\n" );
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document.write( "Let r = the rate of plane A<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(r+50) = the rate of plane B<BR>\n" );
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document.write( "Write a time equation, Time = dist/rate<BR>\n" );
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document.write( "Plane B time - Plane A time = 1 hr<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2000%2F%28%28r%2B50%29%29 ALIGN=MIDDLE  ALT=\"2000%2F%28%28r%2B50%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1400%2Fr ALIGN=MIDDLE  ALT=\"1400%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "Multiply by r(r+50); results<BR>\n" );
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document.write( "2000r - 1400(r+50) = r(r+50)<BR>\n" );
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document.write( "2000r - 1400r - 70000 = r^2 + 50r<BR>\n" );
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document.write( "600r - 70000 = r^2 + 50<BR>\n" );
document.write( "Arrange as a quadratic equation<BR>\n" );
document.write( "0 = r^2 + 50r - 600r + 70000<BR>\n" );
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document.write( "r^2 - 550r + 70000 = 0<BR>\n" );
document.write( "Factor <BR>\n" );
document.write( "(r - 350)(r - 200) = 0<BR>\n" );
document.write( "Two solutions<BR>\n" );
document.write( "r = 200 mph for plane A; then 250 mph for plane B<BR>\n" );
document.write( "and<BR>\n" );
document.write( "r = 350 mph for plane A; then 400 mph for plane B<BR>\n" );
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document.write( "Both these solutions will work<BR>\n" );
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document.write( "Find the times when Plane A = 200 mph<BR>\n" );
document.write( "B: 2000/250 = 8 hr<BR>\n" );
document.write( "A: 1400/200 = 7 hr<BR>\n" );
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document.write( "find the times when Plane A = 350 mph<BR>\n" );
document.write( "B: 2000/400 = 5 hr<BR>\n" );
document.write( "A: 1400/350 = 4 hr </SPAN>\n" );
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