Question

Driving 300 miles through the prairie, the car averaged 30 miles per gallon, while driving 300 miles through the Rocky Mountains; it averaged 20 miles per gallon. What mileage did the car average for all 600 miles?

Answer 1

Hint: To obtain the average mileage of the car for 600 miles we will firstly find the value of gallon for per mile than multiply it by 300 to get the amount of gallon for the driving through prairie then we will multiply the gallon per mile by the next 300 miles through rocky mountains and get the amount of gallon. Now add the gallon used in whole travel and divide the total distance by it to get the desired answer.

Complete step by step answer:
It is given to us that driving miles through the prairie, the car averaged 30 miles per gallon.
So we can write that:
1 gallon $=30$ miles
$\Rightarrow 30$ Miles $=1$ gallon
$\therefore 1$ Mile $=\dfrac{1}{30}$ gallon….$\left( 1 \right)$
Now we have to find the gallon used in 300 miles distance in prairie so we will multiply 300 by equation (1) and get,
$\Rightarrow 300$ Miles $=\dfrac{1}{30}\times 300$ gallons
$\Rightarrow 300$ Miles $=10$ gallons….$\left( 2 \right)$
Next it is given that driving miles through the Rocky Mountains; the car averaged 20 miles per gallon.
So we can write that:
1 gallon $=20$ miles
$\Rightarrow 20$ Miles $=1$ gallon
$\therefore 1$ Mile $=\dfrac{1}{20}$ gallon….$\left( 3 \right)$
Now we have to find the gallon used in 300 miles distance in prairie so we will multiply 300 by equation (3) and get,
$\Rightarrow 300$ Miles $=\dfrac{1}{20}\times 300$ gallons
$\Rightarrow 300$ Miles $=15$ gallons….$\left( 4 \right)$
On adding equation (2) and (40 we get the total gallons used as:
$\begin{align}
  & \Rightarrow 10+15 \\
 & \Rightarrow 25 \\
\end{align}$
So the car used 25 gallons in a 300 miles drive.
Miles per gallon = Total miles/total gallons
Miles per gallon $=\dfrac{600}{25}$
Miles per gallon $=24$
Hence the car gave 24 miles per gallon average for all 600 miles.

Note: To solve this type of question we have to find the total distance and total gallons a car is taking for the whole route. So for that we need to find the value for each mile differently using the data given and not directly add the gallons value and use it to find the answer as we will get the wrong answer in that case.