Average of two trips

Question

Question

While Driving from City A to City B,a car got 22 miles per gallon and while returning on the same road, the car got 30 miles/gallon. What is the car's average mileage for entire trip in miles per gallon?

I thought the answer would be a simple average of 26 but its not. How to solve this problem?

Answer 1

Hint. Let the distance between the cities be $x$ miles. Then

• the number of gallons used on the first trip is . . .
• the number of gallons used on the second trip is . . .
• so the overall miles per gallon is $$\frac{2x}\cdots=\cdots$$

See if you can fill in the dots and hence solve the problem.

For extra credit ;-)

• explain why the actual value of $x$ doesn't matter;
• explain clearly why $26$ is not the right answer.

Answer 2

Let's say that the distance from A to B is 100 miles.

The car will consume 100/22 = 4.54545 gallons on the way out, and 100/30 = 3.3333... on the way back. The average gallons per trip would then be (4.54545+3.3333...)/2 = 3.93939. So for the 100 miles trip / 3.93939 gallons, the car drives an average of 25.3846 miles/gallon. This works regardless of the distance - you can try different values to test it out.