document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208606>Question 1208606</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Every day Jane and Bill both drive into a parking lot, and then take a subway to get to work. Jane drives 22km at 50km/h, and then takes a northbound subway that averages 30 km/h for 14 km, while Bill drives 30 km at 60 km/h and then takes a southbound subway that averages 20km/h for 6 km. It takes each of them 10 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( "Jane driving:<BR>\n" );
document.write( "distance = rate*time<BR>\n" );
document.write( "d = r*t<BR>\n" );
document.write( "22 = 50t<BR>\n" );
document.write( "t = 22/50 = 0.44 of an hour<BR>\n" );
document.write( "0.44 hr = 0.44*60 = 26.4 minutes<BR>\n" );
document.write( "Each decimal value is exact and hasn't been rounded.\r<BR>\n" );
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document.write( "Jane on the subway:<BR>\n" );
document.write( "d = r*t<BR>\n" );
document.write( "14 = 30t<BR>\n" );
document.write( "t = 14/30 of an hour <BR>\n" );
document.write( "That converts to (14/30)*60 = 28 minutes\r<BR>\n" );
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document.write( "Jane drives for 26.4 minutes, there's the 10 minute gap from car to subway, and then she's on the subway for 28 minutes.<BR>\n" );
document.write( "Total = 26.4+10+28 = 64.4 minutes.<BR>\n" );
document.write( "Round this up to 65 minutes. <BR>\n" );
document.write( "If we went with 64 minutes, then we'd miss out on that extra 0.4 of a minute.\r<BR>\n" );
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document.write( "8:30 AM - 65 min<BR>\n" );
document.write( "= (8 hrs + 30 min) - (60 min + 5 min)<BR>\n" );
document.write( "= (8 hrs + 30 min) - (1 hr + 5 min)<BR>\n" );
document.write( "= 8 hrs + 30 min - 1 hr - 5 min<BR>\n" );
document.write( "= (8 hrs - 1 hr) + (30 min - 5 min)<BR>\n" );
document.write( "= 7 hr + 25 min<BR>\n" );
document.write( "= <font color=red>7:25 AM</font> is when Jane should leave home.<BR>\n" );
document.write( "In other words, subtract off 1 hour from 8 AM to drop to 7 AM. Then we subtract the extra 5 minutes from the 30 to get 25.<BR>\n" );
document.write( "Verification with <a  rel=nofollow HREF=\"https://www.wolframalpha.com/input?i=8%3A30+AM+-+65+min\">WolframAlpha</a>\r<BR>\n" );
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document.write( "Bill driving:<BR>\n" );
document.write( "d = r*t<BR>\n" );
document.write( "30 = 60t<BR>\n" );
document.write( "t = 30/60 = 0.5 hr<BR>\n" );
document.write( "0.5 hr = 0.5*60 = 30 min\r<BR>\n" );
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document.write( "Bill on the subway:<BR>\n" );
document.write( "d = r*t<BR>\n" );
document.write( "6 = 20t<BR>\n" );
document.write( "t = 6/20 = 0.3 hr<BR>\n" );
document.write( "0.3 hr = 0.3*60 = 18 min\r<BR>\n" );
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document.write( "Bill's total duration is 30+10+18 = 58 minutes\r<BR>\n" );
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document.write( "Tutor ikleyn has made an error in her calculation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2F%28%28red%2830%29%2F60%29%29+%2B+6%2F%28%2820%2F60%29%29+%2B+10+=+88 ALIGN=MIDDLE  ALT=\"30%2F%28%28red%2830%29%2F60%29%29+%2B+6%2F%28%2820%2F60%29%29+%2B+10+=+88\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "should be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2F%28%28red%2860%29%2F60%29%29+%2B+6%2F%28%2820%2F60%29%29+%2B+10+=+58 ALIGN=MIDDLE  ALT=\"30%2F%28%28red%2860%29%2F60%29%29+%2B+6%2F%28%2820%2F60%29%29+%2B+10+=+58\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The item in red is Bill's driving speed in km/hr.\r<BR>\n" );
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document.write( "8:30 AM - 58 min<BR>\n" );
document.write( "= (8 hrs + 30 min) - (60 min - 2 min)<BR>\n" );
document.write( "= (8 hrs + 30 min) - (1 hr - 2 min)<BR>\n" );
document.write( "= 8 hrs + 30 min - 1 hr + 2 min<BR>\n" );
document.write( "= (8 hrs - 1 hr) + (30 min + 2 min)<BR>\n" );
document.write( "= 7 hrs + 32 min<BR>\n" );
document.write( "= 7:32 AM is when Bill should leave home<BR>\n" );
document.write( "Verification with <a  rel=nofollow HREF=\"https://www.wolframalpha.com/input?i=8%3A30+AM+-+58+min\">WolframAlpha</a>\r<BR>\n" );
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document.write( "To recap, <BR>\n" );
document.write( "Jane should leave home at 7:25 AM<BR>\n" );
document.write( "Bill should leave home at 7:32 AM<BR>\n" );
document.write( "Jane should leave 7 minutes earlier compared to bill (because 32-25 = 7).\r<BR>\n" );
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document.write( "Answer: <BR>\n" );
document.write( "<font color=red>Jane</font> leaves the earliest, and does so at <font color=red>7:25 AM</font><BR>\n" );
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