document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=493883>Question 493883</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi my name is Diala. I'm 13 in Algebra 1 (8th grade). My problem is kind of long, but here it is (I'm stuck on it!):\r<BR>\n" );
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document.write( "11. A jet leaves the Charlotte, North Carolina, airport traveling at an average rate of 564 km/hr. Another jet leaves the airport on half hour later traveling at <BR>\n" );
document.write( "744 km/hr in the same direction. How long will it take the second jet to overtake the first?\r<BR>\n" );
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document.write( "I can probably solve it, but in my head with a scratch sheet of paper just to do any addition, division, etc. Can you please show/tell the work? Cause my problem is to show the work the way my teacher wants it. Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #335505 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=335505\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rate * time = distance.\r<BR>\n" );
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document.write( "the first plane has traveled at 564 km/hr for 1/2 hours before the second plane starts.\r<BR>\n" );
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document.write( "this puts the first plane at 1/2 * 564 = 282 kilometers ahead of the second plane when it starts.\r<BR>\n" );
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document.write( "the second plane needs to close the gap.\r<BR>\n" );
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document.write( "the speed of the second plane is equal to 744 km/hr.\r<BR>\n" );
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document.write( "subtract 564 km/hr from 744 km/hr and you find that the second plane is traveling 180 km/hr faster than the first plane.\r<BR>\n" );
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document.write( "the second plane needs to cover the gap of 282 kilometers.\r<BR>\n" );
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document.write( "rate * time = distance.\r<BR>\n" );
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document.write( "this translates to 180 km/hr * time = 282 km.\r<BR>\n" );
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document.write( "divide both sides of this equation by 180 km/hr to get:\r<BR>\n" );
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document.write( "time = 282 / 180 = 1.566667 hours.\r<BR>\n" );
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document.write( "the second plane will catch up to the first plane in 1.566667 hours.\r<BR>\n" );
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document.write( "another way of looking at this problem is:\r<BR>\n" );
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document.write( "first plane is traveling at 564 km / hr.<BR>\n" );
document.write( "second plane is traveling at 744 km / hr.\r<BR>\n" );
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document.write( "first plane is in the air 1/2 hour longer than the first plane.\r<BR>\n" );
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document.write( "when the second plane catches up with the first plane, they will both have traveled the same distance.\r<BR>\n" );
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document.write( "we call that distance \"d\".\r<BR>\n" );
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document.write( "the first plane is in the air a half hour longer than the first plane, so:\r<BR>\n" );
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document.write( "we let x = hours the second plane is in the air.\r<BR>\n" );
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document.write( "this make x + .5 the number of hours the first plane is in the air.\r<BR>\n" );
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document.write( "note that 30 minutes is equal to 1/2 hour = .5 hours.\r<BR>\n" );
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document.write( "rate * time = distance.\r<BR>\n" );
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document.write( "for the first plane, this equation becomes:\r<BR>\n" );
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document.write( "564 * (x + .5) = d\r<BR>\n" );
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document.write( "for the second plane, this equation becomes:\r<BR>\n" );
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document.write( "744 * x = d\r<BR>\n" );
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document.write( "both equations are equal to d, so we can make them equal to each other to get:\r<BR>\n" );
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document.write( "564 * (x + .5) = 744 * x\r<BR>\n" );
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document.write( "simplify this equation to get:\r<BR>\n" );
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document.write( "564 * x + 282 = 744 * x\r<BR>\n" );
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document.write( "subtract 564 * x from both sides of this equation to get:\r<BR>\n" );
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document.write( "282 = 744 * x - 564 * x\r<BR>\n" );
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document.write( "this becomes:\r<BR>\n" );
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document.write( "282 = 180 * x\r<BR>\n" );
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document.write( "divide both sides of this equation by 180 to get:\r<BR>\n" );
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document.write( "282 / 180 = x\r<BR>\n" );
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document.write( "simplify to get x = 1.566666667 hours\r<BR>\n" );
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document.write( "both ways get the same answer.\r<BR>\n" );
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document.write( "in 1.56666667 hours, the first plane will have traveled 564 * 1.566666657 = 883.6 kilometers.\r<BR>\n" );
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document.write( "in 1.56666667 hours, the second plane will have traveled 744 * 1.566666667 = 1165.6 kilometers.\r<BR>\n" );
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document.write( "the second plane has traveled 1165.6 - 883.6 = 282 kilometers more than the first plane in 1.5666667 hours.\r<BR>\n" );
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document.write( "at that point in time, it has caught up with the first plane and is getting set to pass it.\r<BR>\n" );
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document.write( "this looks something like this:\r<BR>\n" );
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document.write( "hour                0          .5                               2.0666667\r\n" );
document.write( "first plan          xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (564 km/hr)\r\n" );
document.write( "second plane                    xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (744 km/hr)\r\n" );
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document.write( "</PRE>\r<BR>\n" );
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document.write( "first plane starts at hour 0<BR>\n" );
document.write( "second plane starts at hour .5<BR>\n" );
document.write( "second plane catches up to first plane at hour 2.1666667<BR>\n" );
document.write( "both planes travel 1165.6 kilometers.<BR>\n" );
document.write( "first plane takes 2.0666667 hours to travel that distance at 564 km/hr.<BR>\n" );
document.write( "second plane takes 1.5666667 hours to travel that distance at 744 km/hr.<BR>\n" );
document.write( "in the first 1/2 hour, the first plane has traveled .5 * 564 = 282 kilometers.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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