document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=515194>Question 515194</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a car and a bus leave from the same spot and drive in opposite directions. the bus is travelling 11mph slower than the car. in 4.25 hours the car and bus are 174 miles apart. find the average speed of the car.     </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #343806 by </B><A HREF=/tutors/aboutme.mpl?userid=drcole><B>drcole(72)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drcole><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=343806\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let s be the average speed of the car.\r<BR>\n" );
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document.write( "Since the bus is traveling 11 mph slower than the car, we can express the average speed of the bus as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+-+11 ALIGN=MIDDLE  ALT=\"s+-+11\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The relationship between distance traveled, average speed, and time is:\r<BR>\n" );
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document.write( "Distance Traveled = (Average Speed)(Time)\r<BR>\n" );
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document.write( "Therefore, after 4.25 hours, the car has traveled\r<BR>\n" );
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document.write( "Distance Traveled by Car = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28s%29%284.25%29+=+4.25s ALIGN=MIDDLE  ALT=\"%28s%29%284.25%29+=+4.25s\"   DISABLED_style= \"max-width:90%; height:auto;\" > miles\r<BR>\n" );
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document.write( "while the bus has traveled\r<BR>\n" );
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document.write( "Distance Traveled by Bus = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28s+-+11%29%284.25%29+=+4.25s+-+46.75 ALIGN=MIDDLE  ALT=\"%28s+-+11%29%284.25%29+=+4.25s+-+46.75\"   DISABLED_style= \"max-width:90%; height:auto;\" > miles (distributing the 4.25 in the last step)\r<BR>\n" );
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document.write( "We know that the car and the bus are traveling in opposite directions, and that the distance between them after 4.25 hours is 174 miles.  We can express this fact algebraically as an equation:\r<BR>\n" );
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document.write( "Distance Traveled by Car + Distance Traveled by Bus = 174<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.25s+%2B+4.25s+-+46.75+=+174 ALIGN=MIDDLE  ALT=\"4.25s+%2B+4.25s+-+46.75+=+174\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we solve for s:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8.50s+-+46.75+=+174 ALIGN=MIDDLE  ALT=\"8.50s+-+46.75+=+174\"   DISABLED_style= \"max-width:90%; height:auto;\" > (combine like terms)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8.50s+=+220.75 ALIGN=MIDDLE  ALT=\"8.50s+=+220.75\"   DISABLED_style= \"max-width:90%; height:auto;\" > (add 46.75 to both sides)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+=+220.75%2F8.50+ ALIGN=MIDDLE  ALT=\"+s+=+220.75%2F8.50+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (divide both sides by 8.50)\r<BR>\n" );
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document.write( "So we get that the average speed of the car is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=220.75%2F8.50 ALIGN=MIDDLE  ALT=\"220.75%2F8.50\"   DISABLED_style= \"max-width:90%; height:auto;\" > mph, or, to the nearest hundredth, 25.97 mph.  Does this make sense?  If the car is traveling at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=220.75%2F8.50 ALIGN=MIDDLE  ALT=\"220.75%2F8.50\"   DISABLED_style= \"max-width:90%; height:auto;\" > mph, after 4.25 hours it will have traveled <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28220.75%2F8.50%29%284.25%29+=+110.375+miles.++The+bus+is+traveling+11+mph+slower%2C+or+%28to+the+nearest+hundredth%3A%0D%0A%0D%0A%7B%7B%7B220.75%2F8.50+-+11+=+14.97 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > mph\r<BR>\n" );
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document.write( "After 4.25 hours then, the bus has traveled:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28220.75%2F8.50+-+11%29%2A4.25+=+63.625 ALIGN=MIDDLE  ALT=\"%28220.75%2F8.50+-+11%29%2A4.25+=+63.625\"   DISABLED_style= \"max-width:90%; height:auto;\" > miles\r<BR>\n" );
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document.write( "Therefore the car and the bus will be 110.375 + 63.625 = 174 miles apart after 4.25 hours, so our solution works.\r<BR>\n" );
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