16. The Wall Problem

8 Aug
maths with zombies

…because everything’s better with zombies!

There’s been an outbreak of the zombie disease in Glasgow and Scotland is being over-run. The latest surveillance mission spotted a horde of zombies heading south. They’re currently 125 miles away and are moving at a speed of 3 miles per hour. Scotland is lost and the best way to protect the rest of Britain is to build a defensive barricade on the ruins of the ancient Roman wall which was last used over 1,600 years ago. 750 people can build a one mile long section of ten foot high wall in a day but the wall will need to stretch the entire 73 miles from one side of Britain to the other along the border between Scotland and England if it’s going to keep the zombies out. What’s the minimum number of people you will need to recruit to ensure the wall’s completed before the zombie horde gets to it?

A: 7,884

B: 15,768

C: 31,536

D: 54,750

Scroll down to see the right answer…

What answer did you get?

A: With 7,884 people, you’ll only get 18 and a quarter miles of wall built in time and that will hardly keep the zombies out, will it?

B: With 15,793 people, you’ll only get half the wall built before the zombies get there, and half a wall is little better than no wall at all.

C: That’s right. with 31,536 people you’ll just get the last brick in place as the zombies reach the wall.

D: With 54,750, you’ll get the wall built with plenty of time to spare, but maybe all those extra people could have been doing something else instead.

How to work it out: The first thing you need to work out is how long it will take the zombies to reach you. If you divide the distance they have to travel (125 miles) by the speed they are moving at (3 miles an hour), you’ll find it will take the zombie horde 41.67 hours to reach you. This means you have to have the wall finished in 41.67 hours, or (if we divide this by the number of hours in a day – 24) 1.74 days. Next, you need to work out how many people you would need to finish the wall in this time. 750 people can build one mile of wall in a day, but the wall needs to be 73 miles long. If you multiply these two numbers together, you’ll find that 54,650 people could build the whole wall in one day. Except you have 1.74 days and not just one day, so you need to divide this number by 1.74 to get the number you need to complete the wall before the zombies get there, and this is 31,536 people. That’s a lot of people, so you’d better start recruiting them right away!

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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