• Distance = Rate X Time

  "Distance" word problems, often also called "uniform rate" problems, involve something travelling at some fixed steady pace, or else at some average speed.

  Whenever you read a problem that involves "how fast", "how far", or "for how long", you should think of the distance equation, d = r t , where d stands for distance, r stands for (constant or average) rate of speed, and t stands for time.

  Make sure that the units for time and distance agree with the units for the rate. For instance, if they give you a rate of feet per second, your time must be in seconds and your distance must be in feet. Sometimes they try to trick you by using the wrong units, and you have to catch this and convert to the correct units.

  If any 2 items of distance rate or time are given you can calculate the third.

  Example:

  distance time are given

  1. John drove 263.5 miles. It took him 4 hours and 15 minutes.

  What was his average speed? ( miles per hour)

  d                = r                                   t

  263.5 =    rate       ( 4 hours and 15/60   (60 minutes in an hour)     = 4 .25 hour   

  263.5 = 4.25 r

  263.5/4.25  = 4.25/4.25  r        divide each side by 4.25  to solve for r

  62 mph = r

   

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