document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201012>Question 1201012</A>: <I><SPAN STYLE=\"word-break: break-all;\"> three airports, A, B, and C, are located in a north-south line. b is 645 mi north of A, and C is 540 mi north of B. a pilot flew from A to B, delayed 2 h, and continued to C,. the wind was blowing from the south at 15 mi/h during the first part of the trip, but during the delay it changed to the north with a velocity of 20 mi/h. if each flight required the same time, find the airspeed of the plane.<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 #835269 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=835269\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Let's draw a vertical number line to represent the locations of airports A, B, and C. <BR>\n" );
document.write( "The order from top to bottom is: C, B, A.<BR>\n" );
document.write( "We'll also mark the distances between each adjacent airport.<BR>\n" );
document.write( "Each distance is in miles.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C+200%2C+-5%2C5%2C-4%2C4%2C%0D%0Aline%280%2C-3-3%2C0%2C3%2B3%29%2C%0D%0Aline%280.2%2C-3%2C-0.2%2C-3%29%2C%0D%0A%0D%0Aline%280.2%2C0%2C-0.2%2C0%29%2C%0D%0A%0D%0Aline%280.2%2C3%2C-0.2%2C3%29%2C%0D%0Alocate%28-0.5%2C-2.5%2C%22A%22%29%2C%0D%0Alocate%28-0.5%2C0.5%2C%22B%22%29%2C%0D%0Alocate%28-0.5%2C3.5%2C%22C%22%29%2C%0D%0A%0D%0Alocate%28-0.75%2C-1%2C%22645%22%29%2C%0D%0Alocate%28-0.75%2C2%2C%22540%22%29%2C%0D%0A%0D%0Alocate%283%2C-3%2Cmatrix%281%2C2%2CDiagram%2Cnot%29%29%2C%0D%0Alocate%283%2C-3.5%2Cmatrix%281%2C2%2Cto%2Cscale%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add in the wind blowing from the south (i.e. the wind is blowing toward the north) at 15 mph.<BR>\n" );
document.write( "This applies only when the plane is going from A to B.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C+200%2C+-5%2C5%2C-4%2C4%2C%0D%0Aline%280%2C-3-3%2C0%2C3%2B3%29%2C%0D%0Aline%280.2%2C-3%2C-0.2%2C-3%29%2C%0D%0A%0D%0Aline%280.2%2C0%2C-0.2%2C0%29%2C%0D%0A%0D%0Aline%280.2%2C3%2C-0.2%2C3%29%2C%0D%0Alocate%28-0.5%2C-2.5%2C%22A%22%29%2C%0D%0Alocate%28-0.5%2C0.5%2C%22B%22%29%2C%0D%0Alocate%28-0.5%2C3.5%2C%22C%22%29%2C%0D%0A%0D%0Alocate%28-0.75%2C-1%2C%22645%22%29%2C%0D%0Alocate%28-0.75%2C2%2C%22540%22%29%2C%0D%0A%0D%0Ared%28line%281%2C-3%2C1%2C3%29%29%2C%0D%0Ared%28line%281%2C3%2C0.7%2C2.4804%29%29%2C%0D%0Ared%28line%281%2C3%2C1.3%2C2.4804%29%29%2C%0D%0A%0D%0Ared%28locate%281.2%2C0.5%2Cmatrix%281%2C2%2Cwind%2Cspeed%29%29%29%2C%0D%0Ared%28locate%281.2%2C0%2Cmatrix%281%2C2%2C15%2Cmph%29%29%29%2C%0D%0A%0D%0Ablue%28locate%28-4.8%2C3%2Cmatrix%281%2C3%2CWhen%2Cthe%2Cplane%29%29%29%2C%0D%0Ablue%28locate%28-4.8%2C2.5%2Cmatrix%281%2C5%2Cgoes%2Cfrom%2CA%2Cto%2CB%29%29%29%2C%0D%0A%0D%0Alocate%283%2C-3%2Cmatrix%281%2C2%2CDiagram%2Cnot%29%29%2C%0D%0Alocate%283%2C-3.5%2Cmatrix%281%2C2%2Cto%2Cscale%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the plane and the wind are both going north (when the plane goes from A to B), the plane's speed is increased.\r<BR>\n" );
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document.write( "x = speed of the plane with no wind<BR>\n" );
document.write( "x+15 = speed after adding the 15 mph wind boost\r<BR>\n" );
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document.write( "distance = rate*time<BR>\n" );
document.write( "time = distance/rate<BR>\n" );
document.write( "time = (645 miles)/(x+15 mph)<BR>\n" );
document.write( "time = 645/(x+15)<BR>\n" );
document.write( "This is the time, in hours, it takes to go from A to B.\r<BR>\n" );
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document.write( "Side note: <BR>\n" );
document.write( "A headwind slows the plane down (because it attacks the head or front of the plane). <BR>\n" );
document.write( "A tailwind speeds the plane up (because it comes from the tail to push the plane forward).\r<BR>\n" );
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document.write( "------------------------------------------\r<BR>\n" );
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document.write( "When the plane goes from B to C, the wind blows from the north. <BR>\n" );
document.write( "The wind is now aiming south. It moves at 20 mph.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C+200%2C+-5%2C5%2C-4%2C4%2C%0D%0Aline%280%2C-3-3%2C0%2C3%2B3%29%2C%0D%0Aline%280.2%2C-3%2C-0.2%2C-3%29%2C%0D%0A%0D%0Aline%280.2%2C0%2C-0.2%2C0%29%2C%0D%0A%0D%0Aline%280.2%2C3%2C-0.2%2C3%29%2C%0D%0Alocate%28-0.5%2C-2.5%2C%22A%22%29%2C%0D%0Alocate%28-0.5%2C0.5%2C%22B%22%29%2C%0D%0Alocate%28-0.5%2C3.5%2C%22C%22%29%2C%0D%0A%0D%0Alocate%28-0.75%2C-1%2C%22645%22%29%2C%0D%0Alocate%28-0.75%2C2%2C%22540%22%29%2C%0D%0A%0D%0Ared%28line%281%2C3%2C1%2C-3%29%29%2C%0D%0Ared%28line%281%2C-3%2C1.3%2C-2.4804%29%29%2C%0D%0Ared%28line%281%2C-3%2C0.7%2C-2.4804%29%29%2C%0D%0A%0D%0Ared%28locate%281.2%2C0.5%2Cmatrix%281%2C2%2Cwind%2Cspeed%29%29%29%2C%0D%0Ared%28locate%281.2%2C0%2Cmatrix%281%2C2%2C20%2Cmph%29%29%29%2C%0D%0A%0D%0Ablue%28locate%28-4.8%2C3%2Cmatrix%281%2C3%2CWhen%2Cthe%2Cplane%29%29%29%2C%0D%0Ablue%28locate%28-4.8%2C2.5%2Cmatrix%281%2C5%2Cgoes%2Cfrom%2CB%2Cto%2CC%29%29%29%2C%0D%0A%0D%0Alocate%283%2C-3%2Cmatrix%281%2C2%2CDiagram%2Cnot%29%29%2C%0D%0Alocate%283%2C-3.5%2Cmatrix%281%2C2%2Cto%2Cscale%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "At this point the plane's speed x is now decreased to x-20 because it's fighting the wind (the plane goes north while the wind is going south).<BR>\n" );
document.write( "Note: This assumes the plane's speed without wind (x) is the same as before.\r<BR>\n" );
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document.write( "Then,<BR>\n" );
document.write( "distance = rate*time<BR>\n" );
document.write( "time = distance/rate<BR>\n" );
document.write( "time = (540 miles)/(x-20 mph)<BR>\n" );
document.write( "time = 540/(x-20)<BR>\n" );
document.write( "This is the time, in hours, it takes to go from B to C\r<BR>\n" );
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document.write( "To summarize what we know so far:<ul><li>time from A to B = 645/(x+15)</li><li>time from B to C = 540/(x-20)</li></ul>Each time value is in hours.\r<BR>\n" );
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document.write( "The instructions mention \"<font color=blue>each flight required the same time</font>\". <BR>\n" );
document.write( "So we'll set each time expression equal to one another. <BR>\n" );
document.write( "Then solve for x.\r<BR>\n" );
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document.write( "time from A to B = time from B to C<BR>\n" );
document.write( "645/(x+15) = 540/(x-20)<BR>\n" );
document.write( "645(x-20) = 540(x+15)<BR>\n" );
document.write( "645x-12900 = 540x+8100<BR>\n" );
document.write( "645x-540x = 8100+12900<BR>\n" );
document.write( "105x = 21000<BR>\n" );
document.write( "x = 21000/105<BR>\n" );
document.write( "x = <font color=red>200</font>\r<BR>\n" );
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document.write( "The plane's speed without wind is <font color=red>200 mph</font>\r<BR>\n" );
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document.write( "When going from A to B, the time spent is:<BR>\n" );
document.write( "time = 645/(x+15)<BR>\n" );
document.write( "time = 645/(200+15)<BR>\n" );
document.write( "time = 645/215<BR>\n" );
document.write( "time = 3 hours\r<BR>\n" );
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document.write( "When going from B to C, the time spent is:<BR>\n" );
document.write( "time = 540/(x-20)<BR>\n" );
document.write( "time = 540/(200-20)<BR>\n" );
document.write( "time = 540/180<BR>\n" );
document.write( "time = 3 hours\r<BR>\n" );
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document.write( "Both portions of the trip are 3 hours each. This confirms we have the correct answer.\r<BR>\n" );
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document.write( "Answer: The plane's speed without wind is <font color=red>200 mph</font><BR>\n" );
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