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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?

Tim Raczkowski
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user2401175
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  • This question seems to be misleading or wrong. If it were asking in terms of miles per hour, a distorted or weighted average would make sense, but the question seems to be phrasing the two trips as perfectly identical minus the gas mileage. I feel also the answer should be 26. – Brandon Klein Oct 28 '15 at 01:55

2 Answers2

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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.
David
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  • The answer I got is 25.38, but still I am not getting a clear idea of the ques :( – user2401175 Oct 28 '15 at 02:01
  • Why the distance does not matter? Unclear about it – user2401175 Oct 28 '15 at 02:02
  • Have a look at the equation in the middle of my answer. If you fill in the denominator, what happens to the $x$s? – David Oct 28 '15 at 02:03
  • they cancel out..so distances cancel out :) – user2401175 Oct 28 '15 at 02:04
  • Yes exactly, that's why it doesn't matter what $x$ is. – David Oct 28 '15 at 02:05
  • damn,thts so tricky,at first glance I thought I just had to take the average of 22 and 30, thanx a lot for your answer :) – user2401175 Oct 28 '15 at 02:07
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    Re: why answer is not 26. Imagine another scenario. If you drove for 100 miles at 4 miles per gallon and 100 miles at 2000 miles per gallon, then the second trip uses pretty much no fuel, so your overall usage is going to be about 8 miles per gallon (same fuel usage as the first trip, but over twice the distance). It's not going to be very close to 1002. PS if your car gets 2000 miles per gallon, please sell it to me ;-) – David Oct 28 '15 at 02:11
  • I get that now...Man, you are awesome..thanx for that amazing explanation :) – user2401175 Oct 28 '15 at 04:41
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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.

Ole Drews Jensen
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