Rates are mathematical expressions that shows the relationship between two quantities. It shows how changes of one value is causing change to another variable.
A common examples of rates is when growth is compared with time. Time is an important factor when determining rates. For example when we compare rate of growth of a population over a number of years we are comparing number of people that has been added to the population over a certain period of time, maybe six months or one year, probably through birth or immigration.
A business can determine rate of increase of it’s sales by determine the number of sales across given periods of time like months or years.
Another example of rate is speed that determines how object changes it’s distance from point where it started it’s motion to the change of time.
Example
Calculate the rate of change of flow of oil in a pipeline per minute if an 800000 litres storage tank was filled in 4 hours 10mins.
Solution
The number of minutes in 4 hours and 10mins is (4*60)+10 =250mins.
Rate of flow = numbers of liters flowed/ time taken in minutes
Rate of flow=800000/250 hence
Rate of flow= 3200 liters per min
which we can also write as 3200litres/min.
Note:
The above rate of flow could also be expressed in terms of litres per hour where in that case the number of hours will be 4(1/6) hours which can also be expressed as 25/6 hours.
Hence rate of flow in hours will be:
800000liters/(25/6) hours
Which will be (800000/25)*6 and hence rate of flow=192000liters/hour