Question

Janet drove $ 300miles $ in $ 4.5hours $ . How do you write an equation to find the rate at which she was traveling?

Answer 1

Hint: It is known that the rate of change of distance per unit time is called the speed of an object. Using the values given of the distance and time, find the speed Janet.
Speed of an object can be written as, $ v = \dfrac{d}{t} $ where, $ v $ is the speed of the object, $ d $ is the distance covered by the object and $ t $ is the time taken to cover the distance $ d $ .

Complete step by step answer:
We have given here that Janet drove $ d = 300miles $ in $ t = 4.5hours $ .
Now, we know that the rate at which she is travelling is called the speed with which she is travelling. We know that the rate of change of distance per unit time is called the speed of an object. Mathematically it can be written as, $ v = \dfrac{d}{t} $ where, $ v $ is the speed of the object, $ d $ is the distance covered by the object and $ t $ is the time taken to cover the distance $ d $ .
Here we have total distance travelled $ d = 300miles $ and total time taken to travel the distance is $ t = 4.5hours $ .
hence, the rate at which she was travelling i.e. the speed of Janet is,
 $ v = \dfrac{d}{t} $
Or, $ v = \dfrac{{300miles}}{{4.5hours}} $
Calculating the value we have,
 $ v = 66.67miles \cdot h{r^{ - 1}} $
So, the equation which expresses the rate at which she was travelling is $ v = 66.67miles \cdot h{r^{ - 1}} $ .
This is our required answer.

Note:
 $ \bullet $ The average speed of an object is calculated as the total distance travelled by the object divided by the total time taken to cover the distance.
 $ \bullet $ The speed of an object is a scalar quantity. It does not have any direction on the other hand velocity of an object is a vector quantity and it depends on the direction of the object in which it is travelling.