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1. 
   jlcannad Teacher
   High School - 12th Grade

   eNotes Editor

   Start off by picking some variables.  I walk for "x" km.  I cycle for "y" km.  So, x+y=15.  It's a start.

   Now, I start playing with the speeds and time.

   x km at 6km/hour.  If I multiply that, I get km squared over hours. That doesn't help. But if I travel 6 km per hour, that also means in one hour I travel 6 km. I can switch the fraction.  That's important.  If I multiply x km times 1hr/6km, I get that I travel x/6 hours by walking.

   So, I travel x/6 hours walking and y/18 hours cycling.  I do have a time reference.  I traveled a total of one hour and ten minutes.  But I want to have everything in only hours.  So, I traveled 1 and 10/60th of an hour.  So, I can use the improper fraction 1 1/6 or 7/6.

   x/6 + y/18 = 7/6    solving that out....

   3x/18 + y/18 = 21/18

   3x + y = 21

   y = 21 - 3x

   This seems useless until we look at the first equation we wrote... x+y=15

   Every time you see "y," put in what you know y is... 21 - 3x

   x + (21-3x) = 15  Solving, you get x = 3

   So, what the heck is x?  Right up front, we said that I walk for "x" km.  So, if x = 3, I walk for 3 km.

   The hard part to remember is to flip those km/hr fractions so that the "km" measurements cancel each other out.

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   Posted by jlcannad on Saturday January 31, 2009 at 8:05 PM