document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194498>Question 1194498</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A motorist goes for a drive, keeping the reading on the speedometer at a constant value of <BR>\n" );
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document.write( ". The speedometer is assumed to be accurate to ± 2 km h<BR>\n" );
document.write( "−1<BR>\n" );
document.write( ". At the end of the day <BR>\n" );
document.write( "he wants to know how far he has travelled, but unfortunately, he forgot to look at the distance <BR>\n" );
document.write( "indicator when he set out. He thinks that he drove for four hours, give or take a quarter of an <BR>\n" );
document.write( "hour. Estimate how far he travelled and assign an error to your result.  </SPAN>\n" );
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document.write( "It seems like you are trying to write <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 40 \text{ km h}^{-1}\"><BR>\n" );
document.write( "It probably makes more intuitive sense to write it as 40 km/hr or 40 km per hour.\r<BR>\n" );
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document.write( "The driver sees 40 km/hr, but the speedometer has an error of ± 2 km per hour. <BR>\n" );
document.write( "which is the same as writing \"an error of plus/minus 2 km per hour\"\r<BR>\n" );
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document.write( "What this means is that the slowest speed possible is 40-2 = 38 km per hour; while the fastest is 40+2 = 42 km per hour.\r<BR>\n" );
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document.write( "In short, the range of possible speeds is between 38 and 42 km per hour, inclusive of both endpoints.\r<BR>\n" );
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document.write( "The driver also isn't sure how long he drove. He thinks he drove for 4 hours, give or take 1/4 = 0.25 of an hour. <BR>\n" );
document.write( "So the shortest amount of driving time is 4 - 0.25 = 3.75 hours.<BR>\n" );
document.write( "The longest possible driving time is 4+0.25 = 4.25 hours.\r<BR>\n" );
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document.write( "Let's say the driver is going at the slowest speed in that interval (38 km per hour). Let's also say that they drove for the shortest amount of time (3.75 hours)\r<BR>\n" );
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document.write( "Distance = rate*time<BR>\n" );
document.write( "Distance = 38*3.75<BR>\n" );
document.write( "Distance = 142.5 km\r<BR>\n" );
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document.write( "Repeat this for the other possible scenarios. <BR>\n" );
document.write( "Making a two-way table helps organize all four possibilities, but it is of course optional.<BR>\n" );
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document.write( "<tr><TD ></TD><TD >Shortest Time (3.75 hrs)</TD><TD >Longest Time (4.25 hrs)</TD></tr><tr><TD >Slowest Speed (38 km/hr)</TD><TD >38*3.75=142.5</TD><TD >38*4.25=161.5</TD></tr><tr><TD >Fastest Speed (42 km/hr)</TD><TD >42*3.75=157.5</TD><TD >42*4.25=178.5</TD></tr>\n" );
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document.write( "The shortest distance traveled is 142.5 km<BR>\n" );
document.write( "The longest distance traveled is 178.5 km\r<BR>\n" );
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document.write( "Compute the midpoint of those endpoints<BR>\n" );
document.write( "(a+b)/2 = (142.5+178.5)/2 = 160.5\r<BR>\n" );
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document.write( "We estimate that the driver traveled about 160.5 km<BR>\n" );
document.write( "The error is the difference of the midpoint and either extreme<BR>\n" );
document.write( "178.5 - 160.5 = 18<BR>\n" );
document.write( "160.5 - 142.5 = 18<BR>\n" );
document.write( "The error is plus/minus 18 km.<BR>\n" );
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