Archive | September, 2013

21. The Vaccination Program Problem

26 Sep
maths with zombies

…because everything’s better with zombies!

Two months ago, a frightening new disease emerged out of nowhere and killed several hundred people in a remote farming community before it was successfully brought under control by the army. Based on the testimony of the few survivors, this disease caused those infected with it to violently attack and bite anyone they could get their hands on. Those who were bitten soon started doing the same and it’s no surprise that this new disease has been dubbed ‘The Zombie Disease’ by news reporters. You’re worried that if a similar outbreak happened in a more heavily populated area, the disease could quickly sweep across the whole country or maybe even the world, before it could be brought under control, and this could bring humanity to an abrupt end.

After many weeks of hard work, you’ve created a virus against this new disease and you’ve calculated that to be effective at stopping any further outbreaks getting out of hand and turning into a full-blown zombie apocalypse, you need to make sure that at least 95% of the population is vaccinated. It takes 6 minutes to give someone a shot and you have a team of 2,500 trained health professionals to administer them, each of whom can work for 16 hours a day. To the nearest whole day, how long will it take to vaccinate enough people in the USA (assuming a population of 250 million) to prevent a zombie apocalypse happening there?

A: 297 days.

B: 396 days.

c: 475 days.

D: 594 days.

Scroll down to see the right answer…









What answer did you get?

A: You’re way off there! You’d twice as many health professionals to get 95% of the population vaccinated in that amount of time.

B: Your team could only get it done that fast if they worked 24 hours a day, and there’s no way they could do that for very long.

C: Something’s gone with your calculations there, or are you only going to give your staff four hours off a night? If they don’t get enough rest they’ll end up making mistakes and you’ll miss your target of having 95% of the population vaccinated.

D: Spot on, but if you’re going to get everyone vaccinated before there’s another outbreak, you’d better get started as soon as possible.

How to work it out: For the vaccination program to be successful, you need to vaccinate 95% of the population, so the first thing you need to do is work out how many people that is. This is done by multiplying 250 million (the total population size) by 0.95 (95% expressed as a decimal fraction). This tells you you’ll need to vaccinate 237.5 million people. Next, you need to work out how long it will take to vaccinate this many people. It takes 6 minutes to administer each vaccine, so the total time is 6 times the number of people to be vaccinated (237.5 million), which is a staggering 1,425 million minutes. However, this isn’t the actual time it will take, because you have 2,500 all of whom can be working at the same time. To work out the actual time, you need to divide the 1,425 million minutes by the number of workers you have on your team (2,500), and that gives you an actual time of 570,000 minutes or, if we divide it by 60 (the number of minutes in an hour), 9,500 hours. Each worker can only work 16 hours a day, so to get the actual number of days it will take, you will need to divide the number of hours required (9,500) by the length of each person’s working day (16 hours), this gives you the required length of your vaccination program in days, which is 593 and three-quarter days, or, to round it up to the nearest whole day, 594 days. As you can see, vaccinating a population against a disease can take a very long time!

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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20. The Containment Zone Problem – Part II

12 Sep
maths with zombies

…because everything’s better with zombies!

You have a unit of 600 men under your command. You’ve set up a containment zone surrounding a square of nine city blocks to contain a zombie outbreak, but somehow one of the undead has broken through your line. You give the order for your men to pull back one block. As before, each block is 50 yards long by 50 yards wide and you still need at least two soldiers for every three yards of your perimeter to ensure it’s secure. Do you still have enough men to guard the containment zone once you’ve pulled back, or should you call for reinforcements?

A: With 600 men, I can still maintain a secure containment zone even if we have to pull back.

B: Once we pull back, the perimeter will be too long for my men to guard effectively. I’ll need to call for reinforcements.

Scroll down to see the right answer…









What answer did you get?

A: That’s the wrong choice. While you had more than enough men to secure a 9 city block area, you don’t have enough to hold the larger containment area and because of your decision the city will be lost to the undead.

B: You got it right. You don’t have enough men to secure the larger containment area and you need to call for reinforcements right away!

How to work it out: Again, this is a relatively easy one to work out. First, you need to work out the size of the area you need to secure. Originally, you were securing a square of 9 city blocks. This means it was 3 blocks long by three blocks wide. If your men pull back one block on all sides, this means the area you’ll be trying to secure will be a square of five by five city blocks. As before, this containment zone has four sides, but now each side is five city blocks long, and each block is 50 yards wide. To work out the length of the perimeter, you just need to multiply these three numbers together (50 yards per block by five blocks per side by four sides). This tells you the total perimeter you need to cover is 1,000 yards. Now you the need to work out the total number of men you’d need to adequately cover this larger perimeter. Just as with the smaller perimeter, you need two men ever three yards. This is the same as saying you need 2/3rd of a man per yard, so you divide 1,000 by 3 and the multiply it by 2, giving a total of 667 men (rounded up to the nearest whole man). You only have 600, so now you have to pull back, the only way you can save the city is to call for reinforcements, so you’d better do it 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.

19. The Containment Zone Problem – Part I

5 Sep
maths with zombies

…because everything’s better with zombies!

There’s been a report of a zombie outbreak on the north side of the city and your unit of 600 men has been sent in to set up a containment zone while others attempt to neutralise the problem. So far the outbreak is limited to a single city block and your containment zone will consist of a one block buffer zone on all sides of the affected area. This means you will have to seal off a square consisting of a total of nine city blocks, each of which is 50 yards long and 50 yards wide. To make sure your defences hold, know you need at least two soldiers for every three yards of your perimeter. You have two choices: set up the containment zone now or wait for reinforcements. If you try to set up the containment zone and you don’t have enough men to man it properly, you risk being over-run and the zombies will take over the city. However, any unnecessarily delay while you wait for reinforcements will give the zombie disease time to spread, making it harder to contain. You’re the one in charge and need to make a decision right now: do you have enough men to set an effective containment zone or should you wait for reinforcements? You have five seconds…

A: Yes, I have more than enough men and the best action is to set up the containment zone right away.

B: I don’t have enough men under my command. It will give the zombie disease time to spread but I need to wait until reinforcements arrive before I can set up an effective containment zone.

Scroll down to see the right answer…









What answer did you get?

A: You made the right decision, with 600 men you have more than enough to station two every three yards around the containment zone’s perimeter.

B: You shouldn’t have waited for reinforcements because you had enough men. This gave the disease time to spread to other city blocks and now you need to set up an even larger containment area. All this because you got your maths wrong!

How to work it out: This is a relatively simple calculation, but the trick is doing in the five seconds you have to make the decision. First, you need to work out the total length of the perimeter of your planned containment zone. The containment zone has four sides, each three city blocks long, and each block is 50 yards long. To work out the length of the perimeter, you just need to multiply these three numbers together (50 yards per block by three blocks per side by four sides). This tells you the total perimeter you need to cover is 600 yards. You the need to work out the total number of men you’d need to adequately cover it. To do this you need two men ever three yards. This is the same as saying you need 2/3rd of a man per yard, so you divide 600 by 3 and the multiply it by 2, giving a total of 400 men. You have 600, so you have more than enough to set up the perimeter right away and without wait for reinforcements.

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.