6. The Injured Friend Problem

23 May
maths with zombies

…because everything’s better with zombies!

You can see the zombies coming towards you. You estimate that they’re moving at about 4 miles an hour. Normally you’d be able to out run them no problem but today your carrying your best friend who’s just broken his leg and can’t walk. This means you can only move at 1 miles an hour (he might be your friend but he’s heavy!). You can see the door to your safe house at the end of the street. It’s 83 yards away. You look back over your shoulder, the zombies are 250 yards behind you. You have two options: You can carry on with your friend but he’ll slow you down or you can abandon him so you can move faster. Will you still make it to your safe house before the zombies get there? (hint: There’s 1,760 yards in a mile).

A: Yes, so the best thing to do is keep carrying my friend.

B: No, so the only way I’ll survive is if I abandon my friend so I can run faster.

Scroll down to see the right answer…

What answer did you get?

A: You got it right. You’ll arrive at the safe house just half a second before the zombies. Just as well you didn’t get it wrong and accidentally go for B.

B: Oh no! You got your maths wrong and now your friends being eaten alive by zombies when you could have made it even without abandoning him. You did get the maths wrong didn’t you? You didn’t just abandon him, did you? Humm, I’m not too sure I trust you any more …

How to work it out: First, the zombies to reach the safe house: They can travel at 4 miles an hour, that’s 7,040 yards (4 * 1760 or the number of yards in a mile). This means they will cover the 333 yards to the safe house (the 83 yards between you and the safe house plus the 200 yards between you and the zombies) in 0.0473 hours. This is worked out by dividing the distance they need to cover (283 yards) by the distance they can travel in an hour (7,040 yards). 0.0473 hours is the equivalent of 2 minutes and 50.3 seconds. You’ve only got 83 yards to cover but you’re moving much slower. You can only cover one mile or 1,760 yards in an hour. You will take 0.0472 hours (83/1,760) to reach the safe house. That’s 2 minutes and 49.8 second meaning you’ll reach safety with just a hair over half a second. If you’d been just one more yard further from the safe house, they’d have got you.

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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