How are unit rates determined?

1 Answer
Apr 27, 2016

Divide one quantity by another quantity to get the unit rate.

Explanation:

Generally for this type of problem we are dealing with two given (or calculable) quantities specified in different units.

Suppose we knew that #24# miles corresponded to #6# hours (perhaps it had taken #6# hours to walk #24# miles).

then the unit rate of miles to hours (the average speed) would be
#color(white)("XXX")(24 " miles")/(6 " hours")=(4" miles")/("hour")# or #4# miles/hour;

and the unit rate of hours to miles (how long it took to walk 1 mile) would be
#color(white)("XXX")(6" hours")/(24" miles")=(1/4 " hour")/("mile")# or #1/4# hour/mile.

Similarly, if #10# boxes of crayons cost #$25#
then the unit price for a box of crayons would be
#color(white)("XXX")($25)/(10 " boxes") = $2.50# / box.

And, if on a map a line #4# cm long represented a road that was #12# kilometers long
then the unit ratio of real distance to map distance would be
#color(white)("XXX")(12" kilometers")/(4" centimeters") = (3" km")/("cm")#