document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=682077>Question 682077</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Vehicle Car A is now passing a truck that is 90 feet long. Vehicle A is traveling 40 mph( or 60 feet per seconds) and truck B is traveling 30mph (or 45 feet per seconds. Vehicle A will being passing maneuver $ seconds behind the trucj to allow the truck to see him.Vehivle A will return to his lane when he is 60 feet ahead of truck B.<BR>\n" );
document.write( "What is the distance between truc B & vehicle A after A passses the truck and return to his lane? And what us the Total amount Vehicle A must travel to complete this maneuver? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #423085 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=423085\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> MY INTERPRETATION OF THE PROBLEM:<BR>\n" );
document.write( "Car A is now passing a truck (truck B) that is 90 feet long.<BR>\n" );
document.write( "Car A is traveling at 60 feet per second all the time,even when changing lanes, and<BR>\n" );
document.write( "truck B is traveling at 45 feet per second all the time.<BR>\n" );
document.write( "Car A will begin the passing maneuver 4 seconds behind the truck,<BR>\n" );
document.write( "meaning 4 seconds before it would hit the truck if it stayed on the same lane.<BR>\n" );
document.write( "Car A will return to his lane when it is 60 feet ahead of truck B,<BR>\n" );
document.write( "meaning when the car's front bumper is 60 feet ahead of the truck's front bumper.<BR>\n" );
document.write( "MY INTERPRETATION OF THE PROBLEM'S QUESTIONS:<BR>\n" );
document.write( "What is the distance (empty space) between truck B & vehicle A after A passes the truck and returns to its original lane?<BR>\n" );
document.write( "What is the total distance vehicle A must travel to complete this maneuver?<BR>\n" );
document.write( " <BR>\n" );
document.write( "THE PROBLEM WITH THIS PROBLEM is that there is too much open to interpretation, so my answers may not be the expected answers.<BR>\n" );
document.write( "It is quite possible that a less realistic approach was expected.<BR>\n" );
document.write( " <BR>\n" );
document.write( "We would use the speeds in feet per second (ft/s) rather than in mph.<BR>\n" );
document.write( "Since the difference between the speed of the car and the speed of the truck is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60-45=15 ALIGN=MIDDLE  ALT=\"60-45=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >ft/s, before passing the truck, the car would be reducing its distance from the truck at a rate of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60-45=15 ALIGN=MIDDLE  ALT=\"60-45=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >ft/s.<BR>\n" );
document.write( "At that rate, in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds, the car would reduce its distance to the truck by<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A15=60 ALIGN=MIDDLE  ALT=\"4%2A15=60\"   DISABLED_style= \"max-width:90%; height:auto;\" >feet, so the car would start the passing maneuver when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60 ALIGN=MIDDLE  ALT=\"60\"   DISABLED_style= \"max-width:90%; height:auto;\" >ft from the truck.<BR>\n" );
document.write( "If I were driving car A, I would drive in the middle of each lane when not changing lanes.<BR>\n" );
document.write( "To change lanes, I would turn at a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=41.4%5Eo ALIGN=MIDDLE  ALT=\"41.4%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > angle towards the other lane.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28160%2C200%2C-47%2C1%2C-5%2C55%2C%0D%0Aarrow%280%2C0%2C0%2C45%29%2Carrow%280%2C0%2C-39.7%2C0%29%2C%0D%0Ared%28arrow%280%2C0%2C-39.7%2C45%29%29%2Clocate%28-12%2C19%2C41.4%5Eo%29%2C%0D%0Alocate%28-30%2C-1%2C%2239.7+ft%2Fs%22%29%2Clocate%28-5%2C36%2C45%29%2C%0D%0Alocate%28-10%2C32%2C%22ft%2Fs%22%29%2C%0D%0Alocate%28-36%2C36%2C60%29%2Clocate%28-38%2C32%2C%22ft%2Fs%22%29%2C%0D%0Agreen%28line%280%2C45%2C0%2C55%29%29%2Cgreen%28line%28-39.7%2C0%2C-47%2C0%29%29%2C%0D%0Agreen%28line%280%2C45%2C-47%2C45%29%29%2Cgreen%28line%28-39.7%2C0%2C-39.7%2C55%29%29%2C%0D%0Agreen%28rectangle%28-39.7%2C0%2C-42.7%2C3%29%29%2Cgreen%28rectangle%280%2C45%2C-3%2C48%29%29%2C%0D%0Agreen%28rectangle%28-39.7%2C45%2C-42.7%2C48%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That way, my <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60 ALIGN=MIDDLE  ALT=\"60\"   DISABLED_style= \"max-width:90%; height:auto;\" >ft/s speed would have a forward component of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45 ALIGN=MIDDLE  ALT=\"45\"   DISABLED_style= \"max-width:90%; height:auto;\" >ft/s, matching the speed of the truck.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2Acos%2841.4%5Eo%29=60%2A0.75=45 ALIGN=MIDDLE  ALT=\"60%2Acos%2841.4%5Eo%29=60%2A0.75=45\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The sideways component of my <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60 ALIGN=MIDDLE  ALT=\"60\"   DISABLED_style= \"max-width:90%; height:auto;\" >ft/s speed would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=39.7 ALIGN=MIDDLE  ALT=\"39.7\"   DISABLED_style= \"max-width:90%; height:auto;\" >ft/s.<BR>\n" );
document.write( "The lane width in my highway would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >ft, and<BR>\n" );
document.write( "at a lateral speed of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=39.7 ALIGN=MIDDLE  ALT=\"39.7\"   DISABLED_style= \"max-width:90%; height:auto;\" >ft/s, I would move <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >ft laterally in<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F39.7=0.3 ALIGN=MIDDLE  ALT=\"12%2F39.7=0.3\"   DISABLED_style= \"max-width:90%; height:auto;\" >seconds.<BR>\n" );
document.write( "While doing the lane changes at that angle (before and after passing the truck), I would spend<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A0.3 ALIGN=MIDDLE  ALT=\"2%2A0.3\"   DISABLED_style= \"max-width:90%; height:auto;\" >seconds moving at the same forward <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45 ALIGN=MIDDLE  ALT=\"45\"   DISABLED_style= \"max-width:90%; height:auto;\" >ft/s speed as the truck.<BR>\n" );
document.write( "In between lane changes, on the passing lane, I would be gaining on the truck,<BR>\n" );
document.write( "advancing forward from being <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds behind the truck<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60 ALIGN=MIDDLE  ALT=\"60\"   DISABLED_style= \"max-width:90%; height:auto;\" >feet),<BR>\n" );
document.write( "to having my front bumper <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60 ALIGN=MIDDLE  ALT=\"60\"   DISABLED_style= \"max-width:90%; height:auto;\" >ft ahead of the front bumper of the truck.<BR>\n" );
document.write( "Since my car is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" >feet long, that would mean my rear bumper would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60-16=44 ALIGN=MIDDLE  ALT=\"60-16=44\"   DISABLED_style= \"max-width:90%; height:auto;\" >feet in front of the front bumper of the truck after passing.<BR>\n" );
document.write( "That would be my answer to the first question, but I do not think that is the expected answer, because it depends on the length of car A, the driver's lane change strategy and the width of the lane.<BR>\n" );
document.write( " <BR>\n" );
document.write( "From the point of view of the truck driver, the truck is not moving, and the car is advancing at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15 ALIGN=MIDDLE  ALT=\"15\"   DISABLED_style= \"max-width:90%; height:auto;\" >ft/s while on the passing lane.<BR>\n" );
document.write( "Also from the point of view of the truck driver, the car covers a distance of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2B90%2B60=210 ALIGN=MIDDLE  ALT=\"60%2B90%2B60=210\"   DISABLED_style= \"max-width:90%; height:auto;\" >feet while moving forward on the passing lane.<BR>\n" );
document.write( "At <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15 ALIGN=MIDDLE  ALT=\"15\"   DISABLED_style= \"max-width:90%; height:auto;\" >ft/s, those <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210 ALIGN=MIDDLE  ALT=\"210\"   DISABLED_style= \"max-width:90%; height:auto;\" >feet would be covered in<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210%2F15=14 ALIGN=MIDDLE  ALT=\"210%2F15=14\"   DISABLED_style= \"max-width:90%; height:auto;\" >seconds.<BR>\n" );
document.write( "The whole passing maneuver would take<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.6%2B14=14.6 ALIGN=MIDDLE  ALT=\"0.6%2B14=14.6\"   DISABLED_style= \"max-width:90%; height:auto;\" >seconds, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.6 ALIGN=MIDDLE  ALT=\"0.6\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the two lane changes, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14 ALIGN=MIDDLE  ALT=\"14\"   DISABLED_style= \"max-width:90%; height:auto;\" >seconds on the fast lane.<BR>\n" );
document.write( "During that time, the truck would have advanced at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45 ALIGN=MIDDLE  ALT=\"45\"   DISABLED_style= \"max-width:90%; height:auto;\" >ft/s, covering<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14.6%2A45=657 ALIGN=MIDDLE  ALT=\"14.6%2A45=657\"   DISABLED_style= \"max-width:90%; height:auto;\" >feet.<BR>\n" );
document.write( "The car would have advanced <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210+feet ALIGN=MIDDLE  ALT=\"210+feet\"   DISABLED_style= \"max-width:90%; height:auto;\" > relative to the truck, advancing<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=657%2B210=867 ALIGN=MIDDLE  ALT=\"657%2B210=867\"   DISABLED_style= \"max-width:90%; height:auto;\" >feet forward during the whole passing maneuver,<BR>\n" );
document.write( "while on a lane shifting trajectory of total length<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14.6%2A60=876 ALIGN=MIDDLE  ALT=\"14.6%2A60=876\"   DISABLED_style= \"max-width:90%; height:auto;\" >feet, and that would be my answer to the second question.<BR>\n" );
document.write( "The two slanted lane change portions of that trajectory would have accounted for <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.6%2A60=36 ALIGN=MIDDLE  ALT=\"0.6%2A60=36\"   DISABLED_style= \"max-width:90%; height:auto;\" >feet.<BR>\n" );
document.write( "During the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14 ALIGN=MIDDLE  ALT=\"14\"   DISABLED_style= \"max-width:90%; height:auto;\" >seconds moving straight forward on the passing lane, the car would have covered<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2A60=840 ALIGN=MIDDLE  ALT=\"14%2A60=840\"   DISABLED_style= \"max-width:90%; height:auto;\" >feet. </SPAN>\n" );
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