document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=389640>Question 389640</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ok...I think I might be confusing myself (lol)...so I just want to check this out with you all...\r<BR>\n" );
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document.write( "\"An airplane is traveling due west at 1240ft/sec and Santa's sleigh is traveling due east at 5450ft/sec...\r<BR>\n" );
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document.write( "A. If Rudolf can spot airplanes 10,000ft ahead of him and Santa's sleigh and an airplane are 25,000ft away from each other, how many seconds will it take Rudolf to spot the airplane?\"\r<BR>\n" );
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document.write( "I'm not sure if I need to add both rates together and then divide the distance (either 25,000ft...10,000ft ...or 15,000ft (25,000-10,000ft)) by both rates and then figure out the time that way...?\r<BR>\n" );
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document.write( "And...\r<BR>\n" );
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document.write( "B. If Santa's sleigh needs 2500ft to turn out of the way of another aircraft, how long does Rudolf have to inform Santa and turn the sleigh if he spots the aircraft when it is 10,000ft away?\r<BR>\n" );
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document.write( "Same problem...I'm not sure if I'm setting up this problem right...\r<BR>\n" );
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document.write( "Is it 10,000-2500= 7500/(5450+1240)=1.12 sec...?\r<BR>\n" );
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document.write( "Thanks for your help! *smiles* </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #276164 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=276164\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = number of seconds that the sleigh and airplane have been traveling\r<BR>\n" );
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document.write( "In this case, a picture is worth a thousand words (and symbols). So let's draw one\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/santassleighvsairplane.png\">\r<BR>\n" );
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document.write( "In the picture above, we can see that Santa has traveled <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5450x ALIGN=MIDDLE  ALT=\"5450x\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet (first segment shown in red). Recall that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=rt ALIGN=MIDDLE  ALT=\"d=rt\"   DISABLED_style= \"max-width:90%; height:auto;\" > (distance = rate*time). In this case, the rate is 5450ft/sec, so r=5450 and he has been traveling for 'x' seconds. So t=x\r<BR>\n" );
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document.write( "Likewise, the airplane has been traveling at a speed of 1240 ft/sec for 'x' seconds as well. So it has traveled <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1240x ALIGN=MIDDLE  ALT=\"1240x\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft (last segment shown in red).\r<BR>\n" );
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document.write( "The final middle segment has a length of 10,000 ft. because we <u>want</u> the distance between the two to be 10,000 ft at t = x seconds.\r<BR>\n" );
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document.write( "Since the entire distance between them is 25,000 ft, this means that the length of the entire red line is 25,000 ft. So the individual pieces must add to 25000.\r<BR>\n" );
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document.write( "So this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5450x%2B10000%2B1240x=25000 ALIGN=MIDDLE  ALT=\"5450x%2B10000%2B1240x=25000\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Let's solve for 'x' to find the time it will take for Rudolf to spot the airplane.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5450x%2B10000%2B1240x=25000 ALIGN=MIDDLE  ALT=\"5450x%2B10000%2B1240x=25000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6690x%2B10000=25000 ALIGN=MIDDLE  ALT=\"6690x%2B10000=25000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6690x=25000-10000 ALIGN=MIDDLE  ALT=\"6690x=25000-10000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000 ALIGN=MIDDLE  ALT=\"10000\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6690x=15000 ALIGN=MIDDLE  ALT=\"6690x=15000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2815000%29%2F%286690%29 ALIGN=MIDDLE  ALT=\"x=%2815000%29%2F%286690%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6690 ALIGN=MIDDLE  ALT=\"6690\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=500%2F223 ALIGN=MIDDLE  ALT=\"x=500%2F223\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2.24215246636771 ALIGN=MIDDLE  ALT=\"x=2.24215246636771\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use a calculator to find the decimal approximation\r<BR>\n" );
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document.write( "So at approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.24215246636771 ALIGN=MIDDLE  ALT=\"2.24215246636771\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds, the sleigh and the airplane will be 10,000 ft apart.\r<BR>\n" );
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document.write( "So it will take about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.24215246636771 ALIGN=MIDDLE  ALT=\"2.24215246636771\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds for Rudolf to spot the airplane.\r<BR>\n" );
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document.write( "b) I'll let you try this part on your own. I recommend using the picture above as a guide. \r<BR>\n" );
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document.write( "Hint: Since the sleigh needs 2500 ft of clearance, the distance between the plane and the sleigh has been reduced to 2500 ft (instead of 10,000). Once you find this new value of t, subtract it from the answer in part a) to find the elapsed time window that Rudolf has (ie the window for his reaction). If you're still stuck, let me know.\r<BR>\n" );
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document.write( "If you need more help, email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=Algebra%20Help\">jim_thompson5910@hotmail.com</a>\r<BR>\n" );
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document.write( "Also, feel free to check out my <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">tutoring website</a>\r<BR>\n" );
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document.write( "Jim </SPAN>\n" );
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