document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1163254>Question 1163254</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The driving distance between Boston and NYC is 220 miles.  At 10:00am, Alecia starts out driving from Boston to NYC and drives at an average speed of 70MPH.  At 11:00am that same day, Burt starts out driving from NYC to Boston on the same route (opposite direction) and he drives at an average speed of 65MPH.  Assuming neither makes any stops along the way: 1) at what time will they pass one another; and 2) how far will each have driven at that point? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #787280 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=787280\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part 1)\r<BR>\n" );
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document.write( "t = number of hours Alecia has been driving<BR>\n" );
document.write( "t - 1 = number of hours Burt has been driving (he starts 1 hour later, so he has been driving 1 hour less)\r<BR>\n" );
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document.write( "using the formula<BR>\n" );
document.write( "distance = rate*time<BR>\n" );
document.write( "we can form the expression 70t to represent how far (in miles) Alecia has driven after t hours.\r<BR>\n" );
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document.write( "Burt's distance expression is 65(t-1)\r<BR>\n" );
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document.write( "The two distance expressions must add to 220 in order for the two drivers to meet<BR>\n" );
document.write( "70t + 65(t-1) = 220<BR>\n" );
document.write( "70t + 65t-65 = 220<BR>\n" );
document.write( "135t-65 = 220<BR>\n" );
document.write( "135t = 220+65<BR>\n" );
document.write( "135t = 285<BR>\n" );
document.write( "t = 285/135<BR>\n" );
document.write( "t = 2.1111111 approximately (the 1's repeat forever)<BR>\n" );
document.write( "Multiply this with 3600 to get <BR>\n" );
document.write( "2.1111111*3600 = 7599.99996 and that rounds to 7600<BR>\n" );
document.write( "The rounding error occurs because the calculator can only hold so much data.\r<BR>\n" );
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document.write( "Therefore, 7600 seconds have elapsed from the time Alecia started driving to the point where the two drivers meet.\r<BR>\n" );
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document.write( "Convert from pure seconds to hours,minutes,seconds format<BR>\n" );
document.write( "7600 seconds = 7560 seconds + 40 seconds<BR>\n" );
document.write( "7600 seconds = (7560/60) minutes + 40 seconds<BR>\n" );
document.write( "7600 seconds = 126 minutes + 40 seconds<BR>\n" );
document.write( "7600 seconds = 120 minutes + 6 minutes + 40 seconds<BR>\n" );
document.write( "7600 seconds = (120/60) hours + 6 minutes + 40 seconds<BR>\n" );
document.write( "7600 seconds = 2 hours + 6 minutes + 40 seconds<BR>\n" );
document.write( "7600 seconds = 2 hours, 6 minutes, 40 seconds\r<BR>\n" );
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document.write( "They will meet 2 hours, 6 minutes, 40 seconds after 10:00 AM\r<BR>\n" );
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document.write( "Perform clock arithmetic to get<BR>\n" );
document.write( "10:00:00 + 02:06:40 = (10+2):(0+6):(0+40)<BR>\n" );
document.write( "10:00:00 + 02:06:40 = 12:06:40\r<BR>\n" );
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document.write( "Starting at 10:00 AM, and fast forwarding the duration of time found above, we arrive at 12:06:40 PM. This is the time when the two drivers meet.\r<BR>\n" );
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document.write( "Answer = <font color=red>12:06:40 PM</font>\r<BR>\n" );
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document.write( "Part 2)\r<BR>\n" );
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document.write( "Use the t value found back in part 1) to get<BR>\n" );
document.write( "A = Alecia's distance traveled<BR>\n" );
document.write( "A = 70*t <BR>\n" );
document.write( "A = 70*2.11111111111111<BR>\n" );
document.write( "A = 147.777777777778 miles approximately\r<BR>\n" );
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document.write( "and<BR>\n" );
document.write( "B = Burt's distance traveled<BR>\n" );
document.write( "B = 65(t-1)<BR>\n" );
document.write( "B = 65(2.11111111111111-1)<BR>\n" );
document.write( "B = 72.222222222222 miles approximately\r<BR>\n" );
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document.write( "Note how <BR>\n" );
document.write( "A+B = 147.777777777778+72.222222222222 = 220<BR>\n" );
document.write( "to help confirm we have the proper t value\r<BR>\n" );
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document.write( "Answer: <font color=red>Alecia has driven about 147.777777777778 miles while Burt has driven about 72.222222222222 miles</font>\r<BR>\n" );
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