# Math help needed: hungry dog question!

*label*Mathematics

*timer*Asked: Mar 8th, 2019

*account_balance_wallet*$5

### Question Description

You’re standing at the center of a circular field of radius R. The field has a low wire fence around it. Attached to the wire fence (and restricted to running around the perimeter) is a large, sharp-fanged, hungry dog who likes to eat any humans he can catch.

You can run at speed v. Unfortunately, the dog can run four times as fast, at 4v. The dog will do his best to catch you if you try to escape the field. What is your running strategy to escape the field without feeding yourself to the dog.

Please explain your solution.

## Tutor Answer

Please find attached the solution to the mathematics problem.

Solution:

Firstly, as we asses the situation to get a strategy to escape the farm we have to look at the

distance that needs to be covered and indeed the speed to cover that distance. If we were to stay in

the center of the circle and run from the dog towards the fence then we would fail. Reason being

if you look at this critically if you run a separation R and the dog running πR then it would mean

that you would take time R/v whilst it would take the dog πR/(4v) meaning that it would arrive

before you at the exit point given that R/v > πR/(4v).

It goes without saying that you should move closer to the edge and start running from there

than running from the center. However, given that the dog id tethered to the fence we have to

determine how far from the inside so you have the advantage over the dog. Assigning a random

letter to the distance between us and the inside to g...

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