Archive | June, 2013

11. The Fork In The Road Problem

27 Jun
maths with zombies

…because everything’s better with zombies!

You’ve been caught out in the open while you were foraging for food. You are at a fork in the road, with the zombies coming from the south and they are 100 yards away from you. You have two options both of which lead to a safe house. On the road to the northeast, the safe house is only a 100 yards away but it’s up a steep hill. To the northwest, the safe house is further away (some 300 yards) but it’s all downhill. You know you can run at 11.25 miles an hour downhill but only 7.5 miles an hour uphill. The zombies are relentless and can move at 15 miles an hour regardless of whether it’s uphill or downhill. Which way should you go? (Hint: There’s 1,760 yards in a mile).

A: I’d go northwest, it’s further but I can run faster downhill so I’d get there quicker.

B: I’d go northeast. The safe house is nearer so even though I can run slower uphill, I’d get there quicker.

C: It doesn’t matter which way I go, I’ll always make it to a safe house first as long as I don’t waste time trying to work out which way I should go.

D: It doesn’t matter which way I go, given how fast the zombies can run they’ll always get me before I reach a safe house.

E: It will be a dead heat. We’ll all reach the door at the same time but that doesn’t matter because I’ll still end up dead – in the case of a draw, the zombies will always win!

Scroll down to see the right answer…









What answer did you get?

A: Unlucky, the zombies will arrive at the northwest safe house at the same time you did, and this meant they’ll eat you before you get inside.

B: Unlucky, the zombies will arrive at the northeast safe house at the same time you did, and this meant they’ll eat you before you get inside.

C: Something went wrong with your maths there, you can’t make it to either safe house before the zombies get to you.

D: You’re right that it doesn’t matter which safe house you head for, but your maths seems to have gone wrong because you’ll reach the safe house at the same time as the zombies.

E: Spot on! You got the maths right, but that’s not going to be much consolation to you. Since you’ll all arrive at the safe house at the same time, you won’t have time to get inside so you’ll end up dead despite the fact you got the maths right.

How to work it out: You need to work out four things: how long it will take you to each safe house, and then how long it will take the zombies to reach each safe house. In all cases, the maths is the same. First you work out the distance you need to cover and then divide this by the speed. For example, for you to get to the safe house to the northeast, you need to cover 100 yards, but your speed is only 7.5 miles an hour. First convert the speed from miles and hour to yards an a second. This is done by multiplying the speed by the number of yards in mile (1,760) and then dividing it by the number of seconds in an hour (3,600). By doing this, you can work out that 5 miles an hour is the same as 3.67 yards a second. You then divide the distance you need to cover (100 yards in this case) by this number, and you find you’ll reach the northeast safe house in 27.27 seconds. When you do this for the other safe house, you’ll find it’ll also take you 54.55 seconds to reach it. The zombies have to travel further (200 yards to the northeast safe house and 400 yards to the northwest safe house), but they can also move faster. Travelling at 15 miles per hour, it will take then 27.27 to reach the nearer safe house and 54.55 to reach the one that’s further away This means that no matter which way you go, you and the zombies will both reach the door of your chosen safe house at the same time. You’re pretty much screwed either way!

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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10. The Disappearing Zombies Problem

20 Jun
maths with zombies

…because everything’s better with zombies!

The apocalypse has come and, with the exception of a few small, scattered groups of survivors, the entire population of the world has been turned into zombies. That means there’s 7 billion undead walking around, looking for human flesh to feast on. You’re lucky enough to be holed up in an old military bunker you stumbled upon while escaping from the city. You know that zombies, being re-animated dead bodies, will eventually rot away, making it safe for you to go outside again. You work out that zombies have a half-life of 28 days. This means that every 28 days the number of zombies will decrease by 50%. How long will be before all the zombies are gone and it’s safe for you to go outside again?

A: 364 days.

B: 756 days.

C: 924 days.

D: 1,120 days.

Scroll down to see the right answer…









What answer did you get?

A: Something when wrong with your maths there. There will still be more than a million zombies left and you’ll probably get eaten!

B: That’s a bit too soon. You might get away with it, but there will still be a few zombies wandering around out there.

C: Spot on! The last of the zombies will have rotted away just as you step through the door into the outside world.

D: You’ve got that wrong. You’ll still be huddled in your bunker as all the other survivors are out there staking their claims and re-building civilisation.

How to work it out: The starting point here is 7 billion (the number of zombies in the world when you enter the bunker). To work out how many zombies there’ll be after 28 days, you divide this number by 2. This is 3.5 billion (which is still a lot). After another 28 days, this number will be halved again (giving 1.75 billion). You then repeat this until you get a number that’s less than 1. You will need to do this a total of 33 times. This means that it’ll take 924 days (28 * 33) before the last zombie will have disappeared. That’s 2 years, 6 months, and 13 days (I hope you brought a good book with 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.

9. The Food Supply Problem

13 Jun
maths with zombies

…because everything’s better with zombies!

The zombie apocalypse has come and you find yourself all alone and barricaded into an old house. You don’t know who lived there before but they kept their cupboards well stocked. You count everything that’s in them and find you’ve got 56 cans of food. Unfortunately, they’re all spam but it’s better than nothing. You read the label and find that each can weighs 200g and contains 621 calories. You know you need eat 2,500 calories each day to stay healthy. How many days can you survive on your spam before you have to go outside, where the zombies are, in search of food?

A: 13 days.

B: 15 days.

C: 17 days.

D: 19 days.

Scroll down to see the right answer…









What answer did you get?

A: Spot on, but I’m betting that after almost two weeks, you’ll never want to taste another piece of spam as long as you live!

B: You’re a bit over there and you’ll run out of food a couple of days before you think you will.

C: It might be spam, but it’s not going to last that long.

D: You’re out by almost a quarter. If a zombie apocalypse ever comes maybe you’d better leave someone else in charge of the food supplies!

How to work it out: Firstly, don’t get confused by the information about the weight of each can, you don’t need to know this to work out the answer. Instead, you only need to know the number of calories each can has in it (621). You have a total of 56 cans, and each can contains 621 calories. If you multiply these two numbers together (so that’s 56 * 621), you get the total number of calories contained in all the cans (in this case it’s 34,776). You then divide this number by the number of calories you need to each day (so that’s 34,776 divided by 2,500) and this gives you the number of days the food will last for. In this case it’s 13.9, so sometime on the evening of the 13th day, you’re going to finally run out of food. After that, you’ll have no choice but to go outside to look for more.

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.

8. The Quick Draw Problem

6 Jun
maths with zombies

…because everything’s better with zombies!

You’re on your own in a dark alley when a zombie suddenly spots you. It turns in your direction and charges towards you. It’s twenty feet away and, since it’s one of those pesky new fast zombies, it’s moving at a speed of nine miles an hour. You know it will take you 1.5 seconds flat to draw your gun, aim and fire. Will you have time to kill the zombie before it gets to you? (Hint: There’s 5,280 feet in a mile.)

A: There isn’t enough time to shoot the zombie, I’d better start running.

B: I’ve got enough time so I should stand my ground and kill the zombie.

Scroll down to see the right answer…









What answer did you get?

A: You’d have had enough time so you could have shot the zombie. You might have got the maths wrong, but at least you’re still alive.

B: You made the right decision and now there’s one less flesh-muncher in the world – only another six billion to go!

How to work it out: The zombie is travelling at 9 miles an hour but you need to know how long it will take to cover 20 feet. The first thing you need to do is convert the speed from miles an hour to feet per hour. This is 9 times the number of feet in a mile (5,280) which is 47,520. It’s only got to travel 20 feet to get to you. If you divide the distance it has to cover (20 feet) number by the number of feet it can travel in an hour (47,520), this will tell you how long it will take to cover this distance. In this case it’s 0.0004209. This figure seems odd, but this is because this is the length of time in hours it will take to travel 20 feet. To convert this number into seconds, you need to multiply it by 3,600 (the number of seconds in an hour). This tells you that at 9 miles an hour the zombie will take 1.51524 seconds to reach you. Since you can draw you gun, aim and fire in 1.5 seconds flat, you’ll be able to get your shot off just a fraction of a second before it gets to you. You’d better not miss though, because you’ll only have one chance to kill it before it gets to 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.