suppose, we are given
speed of a car is 25 miles per hour
we know that
one quantity is distance (which is in miles)
other quantity is time (which is in hour)
we can also write speed as
[tex]speed=\frac{distance}{time}[/tex]
so, speed is rate of change of distance with respect to time
so, the rate of change of distance with respect to time is 25 miles per hour
we know that
A rate is a ratio in which the two terms are in different units. Rates are used by people every day, such as when they work 48 hours a week or earn interest every year at a bank. When rates are expressed as a quantity of 1, such as 10 feet per second or 20 miles per hour, they are called unit rates
Example
Lucia worked 40 hours in 5 days
the rate is equal to
[tex]\frac{40}{5}\frac{hours}{days}[/tex]
the unit rate is equal to
[tex]\frac{8}{1}\frac{hours}{day}[/tex]
