document.write( "Question 1161456: I'm studying for the SAT's and this question popped up.\r
\n" ); document.write( "\n" ); document.write( "Corrine drives d miles to her office at an average speed of 50 miles per hour. Returning home, she travels by the same route and averages 60 miles per hour. If her trip home is 10 minutes shorter than her trip to her office, what is the value of d?\r
\n" ); document.write( "\n" ); document.write( "The practice book shows the equations would then be \"+d=50%28t%2B1%2F6%29+\" and \"+d=60%28t%29\". It then shows it would substitute \"+d=50%28t%2B1%2F6%29\" into \"+50%28t%2B1%2F6%29=60t\".\r
\n" ); document.write( "\n" ); document.write( "I just don't understand where they got the 1/6 from in the word problem. Could you please explain where the 1/6 came from so I can better understand how the equation was set up? \n" ); document.write( "
Algebra.Com's Answer #785015 by Edwin McCravy(20066)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "10 minutes is 10/60th or 1/6th of an hour.\r\n" );
document.write( "\r\n" );
document.write( "The way the problem is stated it should be worked this way:\r\n" );
document.write( "\r\n" );
document.write( "                  distance   rate     time\r\n" );
document.write( "going to office      d        50        t    \r\n" );
document.write( "returning home       d        60      t-1/6\r\n" );
document.write( "\r\n" );
document.write( "\"system%28d=50t%2C+d=60%28t-1%2F6%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "This will give the correct answer for d also.\r\n" );
document.write( "\r\n" );
document.write( "The way the practice book did it, requires interpreting it as if were\r\n" );
document.write( "worded this way:\r\n" );
document.write( "\r\n" );
document.write( "Corrine returns d miles from her office at an average speed of 60 miles per\r\n" );
document.write( "hour.  When she left from home, she traveled by the same route and averaged\r\n" );
document.write( "50 miles per hour.  If her trip to the office took her 10 minutes longer\r\n" );
document.write( "than her trip home her office, what is the value of d?\r\n" );
document.write( "\r\n" );
document.write( "The practice book reinterpreted the problem.  The difference is that the\r\n" );
document.write( "practice book considered t to be the time returning so the 10 minutes \r\n" );
document.write( "1/6 of an hour had to be added to make the time going longer.  But the\r\n" );
document.write( "way the problem is stated, we should let t be the time going, so we would\r\n" );
document.write( "subtract the 1/6th of an hour to make the time retuning be shorter by 1/6th\r\n" );
document.write( "of an hour.\r\n" );
document.write( "\r\n" );
document.write( "Both ways are correct, but the best way is to solve it as the problem is\r\n" );
document.write( "stated literally.  Since the problem states that the time is shorter\r\n" );
document.write( "returning, then you should pick t as the time going, for that's the time\r\n" );
document.write( "that we are to make shorter by subtracting.  IOW, why change the problem\r\n" );
document.write( "from one where you make the time shorter to a problem to one where you make\r\n" );
document.write( "the time longer, when the one that was given was the one where you make the\r\n" );
document.write( "time shorter?\r\n" );
document.write( "\r\n" );
document.write( "The moral of the story is:  Don't assume the practice book always gives the\r\n" );
document.write( "most obvious, and best, way to work a problem.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );