Question

A car travels 90 miles on 5 gallons of gas. How do you give the ratio of miles to gallons as a rate in miles per gallon?

Answer 1

Hint: We will find the rate in miles per gallon by dividing the total miles travelled using the given amount of gas. We use a unitary method to calculate the rate of miles per gallon.
* Unitary method helps us to calculate the number of units by dividing the total value of multiple units by the value of a single unit.

Complete step by step solution:
We are given that a car travels 90 miles on 5 gallons of gas.
We can also write this equation in another form
Number of miles travelled by a car using 5 gallons of gas \[ = 90\]
Then using the unitary method we can calculate the number of miles travelled per gallon of gas i.e. number of miles traveled in 1 gallon gas.
\[ \Rightarrow \]Number of miles travelled for 1 gallon of gas \[ = \dfrac{{90}}{5}\]
Cancel the same factors from both the numerator and denominator on the right hand side of the equation.
\[ \Rightarrow \]Number of miles travelled for 1 gallon of gas \[ = \dfrac{{18}}{1}\]
The rate of a car travelling 90 miles with 5 gallons of gas is 18 miles per gallon.

\[\therefore \]Rate in miles per gallon is 18

Note: Many students make the mistake of converting the quantities into units like kilometers, meters, liters etc as they are not much familiar with gallons and miles. Keep in mind here we simply have to calculate the rate of travelling i.e. the average gas used in travelling a mile. Also, always cancel the common factors from the numerator and denominator of fraction so that the answer is in simplest form.
Alternate method:
The ratio of miles to gallons can be calculated by dividing given miles travelled by the car by gallons of gas.
\[ \Rightarrow \]Ratio of miles to gallons \[ = \dfrac{{90}}{5}\]
Cancel the same factors from both numerator and denominator on the right hand side of the equation.
\[ \Rightarrow \]Ratio of miles to gallons \[ = \dfrac{{18}}{1}\]
\[\therefore \]Ratio of miles to gallons \[18:1\]