12. The Prius Vs SUV Problem

4 Jul
maths with zombies

…because everything’s better with zombies!

The dead have risen and you want to get as far away as quickly as possible. You run out your house to look for some transport. You can only find two possible cars: an SUV with its 42 gallon fuel tank two-thirds full and a Prius with 9 gallons of fuel in it. The SUV does 14 mpg (miles per gallon) while the Prius does 36 mpg. Which vehicle will allow you to get further away from the zombie outbreak?

A: I’d take the SUV, it uses more gas per mile, but with all that fuel in the tank, it’ll get you further.

B: I’d take the Prius. There’s less fuel in it but it does more miles to the gallon and that will mean I can get further away.

Scroll down to see the right answer…

What answer did you get?

A: You made the right choice. Despite the fact that it’s less fuel efficient, given the amount of fuel in its tank, you will be able to get further before you run out.

B: While it might be a good choice for the environment, the Prius is a poor choice in this case. While the Prius is more efficient, meaning it can get further per gallon of fuel, the total distance you can drive is less than the SUV.

How to work it out: First you need to work out how far you can drive in the SUV. To do this, you begin by working out how much fuel it has in its fuel tank. The tank can hold 42 gallons when it’s full. If it is currently two-thirds full, it will contain two-thirds of 42 gallons. To work out how much this is, divide 42 by 3 and then multiply the answer by 2. This tells you there’s 28 gallons of fuel in the SUV’s tank. It does 14 miles per gallon, so if you multiply the amount of fuel in its tank (28 gallons) by this number, you will know how far it can travel. In this case, it’s 392 miles. Next, you move onto the Prius. Here, you already know the amount of fuel in the tank (9 gallons), so all you need to do is multiply this number by the number of miles it can do per gallon (36). This gives you 324. So despite its better fuel efficiency, the Prius will only get you 324 miles away from the zombie outbreak, while the SUV will get you 392 miles. That’s another 68 miles the zombies need to travel to get you, and in a zombie apocalypse that could be the difference between living and dying!

Note: While the problems provided here are copyright of Maths With Zombies, if you are a teacher, you can use any of these problems for free in your classes – but please credit Maths With Zombies as the original source (e.g. Downloaded from MathsWithZombies.wordpress.com). You can download a PDF handout of this problem from here.

If you do use this problem in a class, please post a comment here to let me know how you used it and how it was received by your students. These problems cannot be used for any commercial purpose without express written permission.


From the author of For Those In Peril On The Sea, a tale of post-apocalyptic survival in a world where zombie-like infected rule the land and all the last few human survivors can do is stay on their boats and try to survive. Now available in print and as a Kindle ebook. Click here or visit www.forthoseinperil.net to find out more. To download a preview of the first three chapters, click here.

To read the Foreword Clarion Review of For Those In Peril On The Sea (where it scored five stars out of five) click here.


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