Question

How are unit rates determined?

Answer 1

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")`