We'd look for one or the other, not both, depending upon the problem statement.
Note that velocity is a vector quantity; it has both magnitude and direction, such as "5 mph NORTH"
Speed, on the other hand, is a scalar quantity (no direction included).
If you could post an example problem or two, I could comment further.
Note that speed is commonly expressed in miles per hour. If you drive 52 miles in 1.5 hours, your average speed was (52 miles) / (1.5 hours) (which can be simplified and which should have the units of measurement (miles/hr).
