document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72383>Question 72383</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I submitted this problem quite a few days ago and did not get a response. I am resubmitting in hopes to get some help.<BR>\n" );
document.write( "Solve the following word problem. Be sure to show the equation you use for the solution.<BR>\n" );
document.write( "Science and medicine. A bus leaves a station at 1 P.M., traveling west at an average rate of 44 mi/h. One hour later a second bus leaves the same station, traveling east at a rate of 48 mi/h. At what time will the two buses be 274 mi apart?<BR>\n" );
document.write( "This is what I have so far.<BR>\n" );
document.write( "1st bus leaves=1pm travels west at 44 mi/h<BR>\n" );
document.write( "2nd bus leaves=2pm travels east at 48 mi/h<BR>\n" );
document.write( "274 miles apart<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #51750 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=51750\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the distance equation d=rt. You will have two distance equations<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D=44t ALIGN=MIDDLE  ALT=\"d%5B1%5D=44t\"   DISABLED_style= \"max-width:90%; height:auto;\" >The first bus heading west.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D=48%28t-1%29 ALIGN=MIDDLE  ALT=\"d%5B2%5D=48%28t-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >The second bus heading east. (notice how the time is t-1. This is set up because for the first hour since the bus doesn't cover any distance). Now to find out how far each bus is away from each other, you simply add the two distances <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D ALIGN=MIDDLE  ALT=\"d%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D ALIGN=MIDDLE  ALT=\"d%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >. For instance, if one bus is 10 miles out and another is 5 miles out, then they are 10+5=15 miles away from each other.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D%2Bd%5B2%5D=274 ALIGN=MIDDLE  ALT=\"d%5B1%5D%2Bd%5B2%5D=274\"   DISABLED_style= \"max-width:90%; height:auto;\" >Set up equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2844t%29%2B%2848%2A%28t-1%29%29=274 ALIGN=MIDDLE  ALT=\"%2844t%29%2B%2848%2A%28t-1%29%29=274\"   DISABLED_style= \"max-width:90%; height:auto;\" >Now solve for t<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44t%2B48t-48=274 ALIGN=MIDDLE  ALT=\"44t%2B48t-48=274\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=92t-48=274 ALIGN=MIDDLE  ALT=\"92t-48=274\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=92t=274%2B48 ALIGN=MIDDLE  ALT=\"92t=274%2B48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=92t=322 ALIGN=MIDDLE  ALT=\"92t=322\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=322%2F92 ALIGN=MIDDLE  ALT=\"t=322%2F92\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=3.5 ALIGN=MIDDLE  ALT=\"t=3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >So it takes 3 and a half hours for the 2 buses to be 274 miles apart. To fully answer this question, 3 and a half hours after 1 PM is 4:30 PM.<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2844%2A3.5%29%2B%2848%2A%283.5-1%29%29=274 ALIGN=MIDDLE  ALT=\"%2844%2A3.5%29%2B%2848%2A%283.5-1%29%29=274\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=154%2B120=274 ALIGN=MIDDLE  ALT=\"154%2B120=274\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=274=274 ALIGN=MIDDLE  ALT=\"274=274\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If that doesn't help, you can plug t=3.5 into the first equation d=44t (the first bus). You'll see that the first bus traveled 154 miles. For the 2nd bus, instead of the bus travelling 3.5 hours, it travels 2.5 (since it starts an hour later). So thats why you must use t-1 instead of t for the second bus. When you plug in this info, you'll see that the 2nd bus travels 120 miles. If you add these 2 distances, you get 274 miles, which shows that our answer works. Hope this helps. </SPAN>\n" );
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