document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=65329>Question 65329</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A plane flies 720 miles against a steady 30 mi/hr headwind and then returns to the same point with the wind. If the entire trip takes 10 hours, what is the plane’s speed in still air? </SPAN>\n" );
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document.write( "A plane flies 720 miles against a steady 30 mi/hr headwind and then returns to the same point with the wind. If the entire trip takes 10 hours, what is the plane’s speed in still air?<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Let p be plane speed<BR>\n" );
document.write( "Against the wind DATA:<BR>\n" );
document.write( "distance= 720 miles ; Rate= p-30 mph ; time = d/r= 720/(p-30) hrs.<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "With the wind DATA:<BR>\n" );
document.write( "distance =720 miles ; rate = p+30 mph ; time = d/r = 720/(p+30) hrs.<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "EQUATION:<BR>\n" );
document.write( "time with + time against = 10 hrs<BR>\n" );
document.write( "720/(p+30) + 720/(p-30)= 10<BR>\n" );
document.write( "Divide thru by 720 to get:<BR>\n" );
document.write( "1/(p+30) + 1/(p-30)= 1/72<BR>\n" );
document.write( "Multiply thru by (p+30)(p-30) to get:<BR>\n" );
document.write( "p-30+p+30=(1/72)(p^2-900)<BR>\n" );
document.write( "Simplify the left side to get:<BR>\n" );
document.write( "2p=(1/72)(p^2-900)<BR>\n" );
document.write( "Multiply both sides by 72 to get:<BR>\n" );
document.write( "144p=p^2-900<BR>\n" );
document.write( "Rearrange:<BR>\n" );
document.write( "p^2-144p-900=0<BR>\n" );
document.write( "Use the quadratic formula to get:<BR>\n" );
document.write( "p=[144+-sqrt(144^2-4*-900)]/2<BR>\n" );
document.write( "p=[144+-156]/2<BR>\n" );
document.write( "Select the positive solution to get:<BR>\n" );
document.write( "p=[144+156]/2=300/2=150 mph<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );