Question

If a car can travel 400 miles on a 15 gallon tank of gas, how many miles could it travel on a 6 gallon tank of gas?

Answer 1

Hint: For this type of word problem, we use the unitary method to solve it. We start to solve the question by finding out the number of miles a car can travel on a 1 gallon tank of gas. Then, we need to perform cross-multiplication as used in the unitary method and then we simplify the expression to get the number of miles a car could travel on a 6 gallon tank of gas.

Complete step by step solution:
We have been given that a car can travel 400 miles on a 15 gallon tank of gas and need to find the number of miles a car can travel on a 1 gallon tank of gas.

We will be using the Unitary method where we first find out the price of the single unit of commodity and then find the price for the successive units by simply multiplying against the price of a single unit.

We know that on 15 gallon tank of gas, a car can travel 400 miles. So, we have

$\Rightarrow$ 15 gallon $=\;$ 400 miles

$\Rightarrow$ 1 gallon $=\;$ $?\;$

Here, we perform cross multiplication to find out the number of miles a car can travel on 1 gallon tank of gas. On cross multiplying, we get,
$\Rightarrow \dfrac{\left( 1\times 400 \right)}{15}$
Simplifying the above expression, we get,
$\Rightarrow \dfrac{80}{3}$miles
From the above, a car can travel $\dfrac{80}{3}$miles on 1 gallon tank of gas.
Now, we need to find the number of miles a car can travel on a 6 gallon tank of gas.

We know that on a 1 gallon tank of gas, a car can travel $\dfrac{80}{3}$ miles. So, we have
$\Rightarrow$ 1 gallon $=\;$ $\dfrac{80}{3}$miles
$\Rightarrow$ 6 gallon $=\;$ $?\;$

Here, we perform cross multiplication to find out the number of miles a car can travel on a 6 gallon tank of gas. On cross multiplying, we get,
$\Rightarrow 6\times \dfrac{80}{3\times 1}$
Simplifying the above expression, we get 160 miles.
Therefore, a car can travel 160 miles on a 6 gallon tank of gas.

Note: Here in our question, we have used the unitary method. While writing our values from the question in a unitary form, for simplification, always write the things to be calculated on the right-hand side and things known on the left-hand side. We can also use the ratio and proportion method to solve this question. Never forget to write the units of the quantity after the whole evaluation of the question. Units are what defines a quantity. Gallon is used to measure the capacity of fluids or volume and is numerically equal to approximately 3.78541 litres.