13. The Amputation Problem

18 Jul
maths with zombies

…because everything’s better with zombies!

You look at the bite on your hand and know instantly you’ve been infected. You know the virus spreads through your body along your lymph vessels and that once it reaches your heart, it will empty into your blood system and then it will be too late to do anything about it. You know the virus travels through your lymph vessels at 2.8 inches a second and that your arm is 16 inches long. How long do you have to amputate your arm before this ‘treatment’ becomes ineffective because the virus has already reached your heart? (Note: You will need to do the maths and amputate your arm in this time, so you’ll need to work out the correct answer very quickly or you won’t have time to act).

A: 5 seconds

B: 10 seconds

C: 15 seconds

D: 20 seconds

Scroll down to see the right answer…

What answer did you get?

A: That’s right, you only have five seconds to do the maths and amputate your arm before it’s too late.

B: You really think you have that long? You’ll have turned in almost half that time.

C: Something’s gone really wrong with your maths there. Luckily (or unluckily) you won’t live long enough to work out what.

D: Boy, just how slowly do you think this disease spreads? At this rate , you’ll still be reaching for the meat cleaver by the time you turn.

How to work it out: This is a relatively simple calculation. It is just the length of your arm(16 inches) divided by the speed at which the virus spreads along your lymph vessels (2.8 inches per second). This means it will reach the end of your arm in 5.71 seconds. As you can see the maths here is easy. However, you need to make sure you do it fast and accurately. This is because you will need to arrive at the right answer quick enough to take the required action, and you won’t have time to double-check your answer. In real life, this is sometimes the case with maths, and it is the speed at which you can arrive at the right answer that’s important and not just whether you can do the calculation or not.

Note: This problem is based on how real disease, rabies, infects the human body. Rabies is probably as close as we get to a real zombie disease because it’s spread through bites and turns people into violent, crazed attackers. The virus travels along nerves at a consistent speed, meaning you can work out exactly how long it will take to reach someone’s brain once they have been bitten. This is the length of time you have to get medical treatment because once rabies reaches the brain it is pretty much 100% fatal.

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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