document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151526>Question 1151526</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It took Millie a total of 4 hours to drive 75 miles to airport and fly 2100 miles to a city in Mexico. If the plane rate is 12 times faster than her car, how fast did she drive? </SPAN>\n" );
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document.write( "12 times faster than the car? or 12 times AS FAST?<br><BR>\n" );
document.write( "They mean different things, and of course the answers will be different....<br><BR>\n" );
document.write( "If the car's speed is x, then \"12 times AS FAST AS\" the car is 12x.<br><BR>\n" );
document.write( "If the car's speed is x, then \"12 times FASTER THAN\" the car is x, plus 12 more times x, or x+12x = 13x.<br><BR>\n" );
document.write( "Unfortunately, in everyday usage the two phrases are used to mean the same thing.<br><BR>\n" );
document.write( "Nearly always, when you see the phrase \"x times faster than...\" the intended meaning is \"x times as fast as...\".<br><BR>\n" );
document.write( "In this problem, \"12 times as fast as\" gives a \"nice\" answer but \"12 times faster than\" does not.  So we can assume the intended meaning is \"12 times as fast as\".<br><BR>\n" );
document.write( "So....<br><BR>\n" );
document.write( "Let x be the speed of the car; then the speed of the plane is 12x.<br><BR>\n" );
document.write( "The time to drive 75 miles at x mph is 75/x; the time to fly 2100 miles at 12x mph is 2100/(12x).<br><BR>\n" );
document.write( "The total time is 4 hours:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75%2Fx+%2B+2100%2F%2812x%29+=+4 ALIGN=MIDDLE  ALT=\"75%2Fx+%2B+2100%2F%2812x%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Multiply everything by 12x to clear the fractions:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2A75+%2B+2100+=+4%2A12x ALIGN=MIDDLE  ALT=\"12%2A75+%2B+2100+=+4%2A12x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3000+=+48x ALIGN=MIDDLE  ALT=\"3000+=+48x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "You can finish from there....<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );