document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197382>Question 1197382</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Every day, Jane and Bill both drive to a parking lot, and then take a subway to get to work. Jane drives 30 km at 80 km/h, then takes a northbound subway that averages 25 km/h for 15 km while Bill drives 60 km at 100 km/h and then takes a southbound subway that averages 35 km/h for 15 km. It takes each of them 12 minutes to change from car to subway, and they arrive at the same destination at 8:30 a.m. At what time, to the nearest minute, does the earliest of them leave home? </SPAN>\n" );
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document.write( "kph = kilometers per hour\r<BR>\n" );
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document.write( "Jane drives 30 km at 80 kph.\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "distance = rate*time<BR>\n" );
document.write( "time = distance/rate<BR>\n" );
document.write( "time = (30 km)/(80 kph) <BR>\n" );
document.write( "time = 3/8 hour<BR>\n" );
document.write( "She spent 3/8 of an hour driving to the parking lot.\r<BR>\n" );
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document.write( "Then she takes 12 minutes, aka 12/60 = 1/5 of an hour, to go from her car to the subway.<BR>\n" );
document.write( "So far the duration is (3/8)+(1/5) = (15/40)+(8/40) = 23/40 of an hour.\r<BR>\n" );
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document.write( "Then she takes a subway which travels at a rate of 25 kph and travels a distance of 15 km<BR>\n" );
document.write( "time = distance/rate<BR>\n" );
document.write( "time = (15 km)/(25 kph) <BR>\n" );
document.write( "time = 3/5 hour\r<BR>\n" );
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document.write( "Add this to the duration<BR>\n" );
document.write( "(23/40)+(3/5) = (23/40)+(24/40) = 47/40<BR>\n" );
document.write( "Put another way<BR>\n" );
document.write( "3/8 + 1/5 + 3/5 = 47/40\r<BR>\n" );
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document.write( "Her total duration is 47/40 of an hour.<BR>\n" );
document.write( "1/40 of an hour is (1/40)*60 = 1.5 minutes exactly.<BR>\n" );
document.write( "47/40 of an hour is 47*(1/40 hr) = 47*(1.5 min) = 70.5 minutes exactly\r<BR>\n" );
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document.write( "Round up to the nearest minute to get 71 minutes.\r<BR>\n" );
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document.write( "71 min = 60 min + 11 min\r<BR>\n" );
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document.write( "The total duration is 1 hr + 11 min when rounding to the nearest minute.\r<BR>\n" );
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document.write( "She arrives at her destination at 8:30 AM<BR>\n" );
document.write( "Subtract off 1 hour to get to 7:30 AM<BR>\n" );
document.write( "Subtract off a further 11 minutes to get to 30-11 = 19<BR>\n" );
document.write( "I.e. 7:30 AM rewinds back to 7:19 AM after subtracting off those additional 11 minutes.\r<BR>\n" );
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document.write( "Jane needs to leave her home at <font color=red>7:19 AM</font>\r<BR>\n" );
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document.write( "Let's move our attention to Bill.\r<BR>\n" );
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document.write( "He travels 60 km at 100 kph when driving.<BR>\n" );
document.write( "time = distance/rate<BR>\n" );
document.write( "time = (60 km)/(100 kph)<BR>\n" );
document.write( "time = 3/5 hour\r<BR>\n" );
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document.write( "He takes 12 min = 1/5 hour going from his car to the subway\r<BR>\n" );
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document.write( "His subway travels 15 km at a speed of 35 kph<BR>\n" );
document.write( "time = distance/rate<BR>\n" );
document.write( "time = (15 km)/(35 kph) <BR>\n" );
document.write( "time = 3/7 hour\r<BR>\n" );
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document.write( "The three durations of each sub-interval are<BR>\n" );
document.write( "3/5 hour ... home to parking lot<BR>\n" );
document.write( "1/5 hour ... car to subway<BR>\n" );
document.write( "3/7 hour ... subway to work\r<BR>\n" );
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document.write( "Add up those fractions to get the total duration he travels<BR>\n" );
document.write( "3/5+1/5+3/7<BR>\n" );
document.write( "4/5+3/7<BR>\n" );
document.write( "28/35+15/35<BR>\n" );
document.write( "43/35\r<BR>\n" );
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document.write( "Multiply by 60 to convert this to purely minutes only<BR>\n" );
document.write( "43/35 hr = (43/35)*60 = 73.714 min approximately<BR>\n" );
document.write( "Let's round this up to the nearest minute to get 74 minutes.\r<BR>\n" );
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document.write( "74 min = 60 min + 14 min<BR>\n" );
document.write( "74 min = 1 hr + 14 min\r<BR>\n" );
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document.write( "Start at 8:30 AM<BR>\n" );
document.write( "Subtract off 1 hour to get to 7:30 AM<BR>\n" );
document.write( "Subtract off another 14 min to get to <font color=red>7:16 AM</font>\r<BR>\n" );
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document.write( "Or you could note the gap between durations 71 minutes (Jane) and 74 minutes (Bill) is 74-71 = 3 minutes.<BR>\n" );
document.write( "Therefore, Bill needs to leave 3 minutes earlier than Jane does.\r<BR>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "Jane = <font color=red>7:19 AM</font><BR>\n" );
document.write( "Bill = <font color=red>7:16 AM</font><BR>\n" );
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