Question

You can drive your car 21.7 miles with one gallon of gasoline. At that rate, how many miles can you drive with 13.2 gallons of gasoline?

Answer 1

Hint: The rate of burning of gasoline is a ratio defined by the number of miles covered per gallon of gasoline. The rate multiplied by the gallons of gasoline available will give the number of miles that could be covered.
Formula used:
The rate of burning of gasoline is:
$\text{Rate} = \dfrac{\text{ Number of miles covered}}{\text{Gallons of gasoline used}}$.

Complete answer:
We are given that 21.7 miles is covered with 1 gallon of gasoline. This means that the rate of burning of gasoline is:
$Rate = \dfrac{\text{ 21.7 miles}}{\text{ 1 gallon}} = \text{21.7 miles per gallon}$.
Now, the rate multiplied by the gallons of gasoline available gives the miles that can be covered with that amount of gasoline.
$\eqalign{
  & \text{Gallons of gasoline used $\times$ Rate = Number of miles covered}
  & \Rightarrow \text{13.2 gallons $\times$ 21.7 miles per gallon = 286.44 miles.}}
$
Therefore, with 13.2 gallons of gasoline, one can drive the car for 286.44 miles.
Additional information: The rate (y per x or y/x) of any quantity (y) is defined with respect to some other quantity (x) for example, speed is a rate of change of distance with respect to time.
$speed = \dfrac{distance}{time}$.
Likewise, the given question deals with the rate of burning of fuel (or change in gallons of fuel) which is the amount of distance covered per gallon. Another way of defining rate is with the help of derivatives. The rate of change of y with respect to x also can be written as dy/dx. Generally, derivatives are used when we are talking about very small changes in x. Rate also happens to be the slope of a curve.

Note:
One can also handle this question by using ratio and proportions. We are already given how many miles the car can drive for 1 gallon, we need to find the number of miles for 13.2 gallons of gasoline. We can put x in place of the number of miles and find the required answer.