document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195978>Question 1195978</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A motorist leaves Caribou City at 5:03 am, drives the 163 miles to Mooseville , takes a 36 minute break and then drives a further 328 miles to Shellberg, arriving at 8:11 pm.\r<BR>\n" );
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document.write( "A.) Assuming the motorist drives at a constant speed throughout the journey, at what speed (to the nearest mile per hour) does he/she travel?\r<BR>\n" );
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document.write( "B.) If the motorist had gone 5 miles per hour slower than the speed you recorded in part (a), at what time (to the nearest minute) would he or she arrive?\r<BR>\n" );
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document.write( "C.) If the motorist had gone 1 mile per hour faster than the speed you recorded in part (a), at what time (to the nearest minute) would he or she arrive? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #828634 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=828634\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part A\r<BR>\n" );
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document.write( "The gap from 5:03 AM to 8:11 PM is 15 hours, 8 minutes<BR>\n" );
document.write( "This is because...<ul><li>The jump from 5:03 AM to 5:03 PM is 12 hours</li><li>The jump from 5:03 PM to 8:03 PM is another 3 hours (12+3 = 15 hours so far)</li><li>The jump from 8:03 PM to 8:11 PM is another 8 minutes (since 11-3 = 8)</li></ul>That's how I got a total duration of 15 hrs, 8 min. This accounts for actual driving, and the break when the person isn't driving.\r<BR>\n" );
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document.write( "The driver took a 36 minute break.<BR>\n" );
document.write( "Rewrite 36 as 8+28<BR>\n" );
document.write( "I'm doing it like this so we can pull out the 8.\r<BR>\n" );
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document.write( "We'll subtract off those first 8 minutes to get<BR>\n" );
document.write( "(15hr,8min) - (8min) = 15 hrs\r<BR>\n" );
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document.write( "Then subtract off the remaining 28 minutes of that break<BR>\n" );
document.write( "15 hrs - 28 min = (14 hrs + 1 hr) - 28 min<BR>\n" );
document.write( "15 hrs - 28 min = (14 hrs + 60 min) - 28 min<BR>\n" );
document.write( "15 hrs - 28 min = 14 hrs + (60 min - 28 min)<BR>\n" );
document.write( "15 hrs - 28 min = 14 hrs + 32 min\r<BR>\n" );
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document.write( "After ignoring the break, s/he actually spent 14 hrs & 32 min driving.\r<BR>\n" );
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document.write( "Let's convert that figure to hours only<BR>\n" );
document.write( "14 hrs + 32 min = 14 hrs + (32/60 hr)<BR>\n" );
document.write( "14 hrs + 32 min = 14 hrs + 0.533333 hr<BR>\n" );
document.write( "14 hrs + 32 min = 14.533333 hrs<BR>\n" );
document.write( "The decimal value is approximate.\r<BR>\n" );
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document.write( "The total distance traveled was:<BR>\n" );
document.write( "163 mi + 328 mi = 491 mi\r<BR>\n" );
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document.write( "Now we can then say:<BR>\n" );
document.write( "distance = rate*time<BR>\n" );
document.write( "rate = distance/time<BR>\n" );
document.write( "rate = (491 mi)/(14.533333 hrs)<BR>\n" );
document.write( "rate = 33.784404 mph<BR>\n" );
document.write( "This value is approximate.\r<BR>\n" );
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document.write( "Round to the nearest whole number to get 34 mph\r<BR>\n" );
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document.write( "Answer: <font color=red>34 mph</font><BR>\n" );
document.write( "This answer is approximate.\r<BR>\n" );
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document.write( "======================================================<BR>\n" );
document.write( "Part B\r<BR>\n" );
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document.write( "In part A, we found his/her speed to be roughly 34 mph.<BR>\n" );
document.write( "If they go 5 mph slower, then they now have a speed of 34-5 = 29 mph.\r<BR>\n" );
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document.write( "The total distance stays the same.<BR>\n" );
document.write( "Let's compute the time duration spent driving (ignore the 36 min break for now)\r<BR>\n" );
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document.write( "distance = rate*time<BR>\n" );
document.write( "time = distance/rate<BR>\n" );
document.write( "time = (491 mi)/(29 mph)<BR>\n" );
document.write( "time = 16.931034 approximately<BR>\n" );
document.write( "This is the number of hours spent driving.\r<BR>\n" );
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document.write( "Let's convert to hours,minutes format<BR>\n" );
document.write( "16.931034 hr = 16 hr + 0.931034 hr<BR>\n" );
document.write( "16.931034 hr = 16 hr + (0.931034 hr)*(60 min/1 hr)<BR>\n" );
document.write( "16.931034 hr = 16 hr + (0.931034*60) min<BR>\n" );
document.write( "16.931034 hr = 16 hr + 55.86204 min<BR>\n" );
document.write( "16.931034 hr = 16 hr + 56 min<BR>\n" );
document.write( "I rounded to the nearest minute.\r<BR>\n" );
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document.write( "We've yet to include the 36 minute break. <BR>\n" );
document.write( "Let's do so now.<BR>\n" );
document.write( "(16 hr + 56 min) + 36 min<BR>\n" );
document.write( "16 hr + (56 min + 36 min)<BR>\n" );
document.write( "16 hr + (92 min)<BR>\n" );
document.write( "16 hr + (60 min + 32 min)<BR>\n" );
document.write( "16 hr + (1 hr + 32 min)<BR>\n" );
document.write( "(16 hr + 1 hr) + 32 min<BR>\n" );
document.write( "17 hr + 32 min<BR>\n" );
document.write( "This is the total duration from when the motorist left Caribou City to when s/he arrived at Shellberg. \r<BR>\n" );
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document.write( "Rewind the clock back to 5:03 AM<BR>\n" );
document.write( "<ul><li>Add on 12 hours to get to 5:03 PM</li><li>Add on 5 more hours (12+5 = 17 hrs so far) to get to 10:03 PM</li><li>Then add on the final 32 minutes to get to 10:35 PM</li></ul>\r<BR>\n" );
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document.write( "Answer: <font color=red>10:35 PM</font><BR>\n" );
document.write( "This answer is approximate.\r<BR>\n" );
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document.write( "======================================================<BR>\n" );
document.write( "Part C\r<BR>\n" );
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document.write( "The steps shown here are very similar to part B.<BR>\n" );
document.write( "In fact, because of this similarity, I effectively copy/pasted the main outline of the steps. The only main changes are the numbers.\r<BR>\n" );
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document.write( "In part A, we found his/her speed to be roughly 34 mph.<BR>\n" );
document.write( "If they go 1 mph faster, then they now have a speed of 34+1 = 35 mph.\r<BR>\n" );
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document.write( "The total distance stays the same.<BR>\n" );
document.write( "Let's compute the time duration spent driving (ignore the 36 min break for now)\r<BR>\n" );
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document.write( "distance = rate*time<BR>\n" );
document.write( "time = distance/rate<BR>\n" );
document.write( "time = (491 mi)/(35 mph)<BR>\n" );
document.write( "time = 14.028571 approximately<BR>\n" );
document.write( "This is the number of hours spent driving.\r<BR>\n" );
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document.write( "Let's convert to hours,minutes format<BR>\n" );
document.write( "14.028571 hr = 14 hr + 0.028571 hr<BR>\n" );
document.write( "14.028571 hr = 14 hr + (0.028571 hr)*(60 min/1 hr)<BR>\n" );
document.write( "14.028571 hr = 14 hr + (0.028571*60) min<BR>\n" );
document.write( "14.028571 hr = 14 hr + 1.71426 min<BR>\n" );
document.write( "14.028571 hr = 14 hr + 2 min<BR>\n" );
document.write( "I rounded to the nearest minute.\r<BR>\n" );
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document.write( "We've yet to include the 36 minute break. <BR>\n" );
document.write( "Let's do so now.<BR>\n" );
document.write( "(14 hr + 2 min) + 36 min<BR>\n" );
document.write( "14 hr + (2 min + 36 min)<BR>\n" );
document.write( "14 hr + 38 min<BR>\n" );
document.write( "This is the total duration from when the motorist left Caribou City to when s/he arrived at Shellberg.\r<BR>\n" );
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document.write( "Rewind the clock back to 5:03 AM<BR>\n" );
document.write( "<ul><li>Add on 12 hours to get to 5:03 PM</li><li>Add on 2 more hours (12+2 = 14 hrs so far) to get to 7:03 PM</li><li>Then add on the final 38 minutes to get to 7:41 PM</li></ul>\r<BR>\n" );
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document.write( "Answer: <font color=red>7:41 PM</font><BR>\n" );
document.write( "This answer is approximate.<BR>\n" );
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