17. The Tank vs Motorcycle Problem

15 Aug
maths with zombies

…because everything’s better with zombies!

You’ve heard about a safe zone which has been set up and you figure getting there is your best chance of surviving the zombie outbreak in your country. The bad news is that it’s 125 miles away. You have two transport options: a motorbike and a tank. The motorbike‘s much faster and you’ll be able to travel at 60 miles per hour. However, it’s also much more dangerous and there’s a one in six chance you’ll get grabbed by a zombie during each hour you’re on the road. The tank’s a lot slower and can only travel at 7 miles per hour, meaning you’ll be on the road for longer, but it’s also much safer and there’s only a one in fifty chance of a zombie getting you during each hour you are travelling. Which transport option offers you the best chance of getting to the safe zone in one piece?

A: The tank’s slower but safer, so it’s the best option.

B: While the motorbike is less safe, you’ll get there quicker, so overall it’s the best option.

Scroll down to see the right answer…

What answer did you get?

A: Bad choice! There’s a 35.7% chance of you getting caught by a zombie before you reach the safe zone if you choose to travel by tank. This means travelling by tank is marginally more dangerous than travelling by motorbike.

B: Well done, you made the right choice. With a 34.7% chance of getting grabbed by a zombie before you get to the safe zone, the motorbike is safer than the tank.

How to work it out: The key to this problem is working out how long it will take to reach the safe zone using each mode of transport. This is done by dividing the distance you need to travel (125 miles) by the speed of each vehicle. For the tank, this is 125/7 and it means you’ll be on the road for 17.86 hours. For the motorbike, it’s 125/60, meaning you’ll get to the safe zone in 2.08 hours. Now, you can work out the cumulative probability that you’ll get caught by a zombie for each one. For the tank, it’s 1/50 per hour or, if you convert this into a percentage by dividing 1 by 50 and multiplying it by 100, 2%. To get the cumulative probability, you multiply this value by the length of time the journey will take (17.86 hours), which gives you a total chance of falling victim to a zombie before you get to the safe zone of 35.7%. For the motorbike, there’s a 1 in 6 chance of a zombie getting you per hour, or if converted into a percentage, 16.67%. When you multiply this by the time it would take you to get there on the motorbike (2.08 hours) this gives you an overall probability getting killed by a zombie before you get there of 34.7%. Despite the fact there is a far greater risk of you getting caught by a zombie in each hour, the motorbike’s much faster speed means you spend less time on the road, so overall it’s marginally safer.

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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