document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200493>Question 1200493</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A private airplane leaves an airport and flies due east at 192 km/hr. Two hours later, a jet leaves the same airport and flies due east at 960 km/hr. How long after the jet leaves will it overtake the plane?<BR>\n" );
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document.write( "kph = kilometers per hour\r<BR>\n" );
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document.write( "Let's call the planes A and B.\r<BR>\n" );
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document.write( "Plane A travels east at 192 kph<BR>\n" );
document.write( "Plane B travels east at 960 kph, taking off 2 hours later.\r<BR>\n" );
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document.write( "A = slower plane<BR>\n" );
document.write( "B = faster plane\r<BR>\n" );
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document.write( "x = amount of time the faster plane is in the air.\r<BR>\n" );
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document.write( "The slower plane got a 2 hour head start, so x+2 represents the number of hours the slower plane is flying.\r<BR>\n" );
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document.write( "Plane A<BR>\n" );
document.write( "distance = rate*time<BR>\n" );
document.write( "distance = 192*(x+2)\r<BR>\n" );
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document.write( "Plane B<BR>\n" );
document.write( "distance = rate*time<BR>\n" );
document.write( "distance = 960*x\r<BR>\n" );
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document.write( "The faster plane passes the slower one when the two aircraft have traveled the same distance.<BR>\n" );
document.write( "distanceA = distanceB<BR>\n" );
document.write( "192*(x+2) = 960x<BR>\n" );
document.write( "192x+384 = 960x<BR>\n" );
document.write( "384 = 960x-192x<BR>\n" );
document.write( "384 = 768x<BR>\n" );
document.write( "x = 384/768<BR>\n" );
document.write( "x = 0.5\r<BR>\n" );
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document.write( "This leads to x+2 = 0.5+2 = 2.5\r<BR>\n" );
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document.write( "Plane A is in the air for 2.5 hrs (aka 2.5*60 = 150 min, aka 2 hrs + 30 min)<BR>\n" );
document.write( "Plane B is in the air for 0.5 hrs (aka 0.5*60 = 30 min)\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "plane A's distance = 192*2.5 = 480 km<BR>\n" );
document.write( "plane B's distance = 960*0.5 = 480 km<BR>\n" );
document.write( "Both have traveled the same distance, so the answer is confirmed.\r<BR>\n" );
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document.write( "Answer: <font color=red>0.5 hours</font> aka <font color=red>30 minutes</font><BR>\n" );
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