document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=116877>Question 116877</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve.\r<BR>\n" );
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document.write( "Ariana took 2 hours longer to drive 360 miles on the first day of a trip than she took to drive 270 miles on the second day. If her speed was the same on both days, what was the driving time each day?\r<BR>\n" );
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document.write( "Solve. \r<BR>\n" );
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document.write( "A plane flies 720 miles against a steady 30 mile per hour headwind and than returns to the same point with the wind. If the entire trip takes 10 hours, what is the plane's speed in still air?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85089 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=85089\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ariana took 2 hours longer to drive 360 miles on the first day of a trip than she took to drive 270 miles on the second day. If her speed was the same on both days, what was the driving time each day?<BR>\n" );
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document.write( "Let t = time to drive 270 mi<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(t+2) = time to drive 360 mi<BR>\n" );
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document.write( "Speed of the two days is given as equal, so write speed equation:<BR>\n" );
document.write( "Speed = distance/time<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%2F%28%28t%2B2%29%29 ALIGN=MIDDLE  ALT=\"360%2F%28%28t%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=270%2Ft ALIGN=MIDDLE  ALT=\"270%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Cross multiply:<BR>\n" );
document.write( "360t = 270(t+2)<BR>\n" );
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document.write( "360t = 270t + 540<BR>\n" );
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document.write( "360t - 270t = 540<BR>\n" );
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document.write( "90t = 540<BR>\n" );
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document.write( "t = 540/90<BR>\n" );
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document.write( "t = 6 hrs for the 270 mi day<BR>\n" );
document.write( "then<BR>\n" );
document.write( "6 + 2 = 8 hrs for the 360 mi day<BR>\n" );
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document.write( "Check solution by finding if the speeds, are indeed equal:<BR>\n" );
document.write( "360/8 = 45 mph<BR>\n" );
document.write( "270/6 = 45 mph, confirms our solution<BR>\n" );
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document.write( "Solve.<BR>\n" );
document.write( "A plane flies 720 miles against a steady 30 mile per hour headwind and than<BR>\n" );
document.write( " returns to the same point with the wind. If the entire trip takes 10 hours, <BR>\n" );
document.write( "what is the plane's speed in still air? <BR>\n" );
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document.write( "Let s = speed in still air<BR>\n" );
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document.write( "(s+30) = speed with the wind<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(s-30) = speed against the wind<BR>\n" );
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document.write( "Write a time equation; Time = Distance/speed<BR>\n" );
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document.write( "With wind time + against wind time = 10 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720%2F%28%28s%2B30%29%29 ALIGN=MIDDLE  ALT=\"720%2F%28%28s%2B30%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720%2F%28%28s-30%29%29 ALIGN=MIDDLE  ALT=\"720%2F%28%28s-30%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 10<BR>\n" );
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document.write( "Multiply equation by (s+30)(s-30) to eliminate the denominators:<BR>\n" );
document.write( "720(s-30) + 720(s+30) = 10(s-30)(s+30)<BR>\n" );
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document.write( "720s - 21600 + 720s + 21600 = 10(s^2 - 900)<BR>\n" );
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document.write( "1440s = 10s^2 - 9000<BR>\n" );
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document.write( "0 = 10s^2 - 1440s - 900; a quadratic equation:<BR>\n" );
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document.write( "Simplify, divide equation 10<BR>\n" );
document.write( "s^2 - 144s - 900 = 0<BR>\n" );
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document.write( "Fortunately this will factor:<BR>\n" );
document.write( "(s-150)(s+6) = 0<BR>\n" );
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document.write( "s = +150 mph (the only solution that makes sense) in still air<BR>\n" );
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document.write( "Check solution by finding the times.<BR>\n" );
document.write( "with speed = 180; against speed = 120<BR>\n" );
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document.write( "720/120 = 6 hrs<BR>\n" );
document.write( "720/180 = 4 hrs<BR>\n" );
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document.write( "Total hrs:10 hrs, confirms our solution\r<BR>\n" );
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