Math help needed: hungry dog question!

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

School: Duke University

Please find attached the solution to the mathematics problem.

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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awesome work thanks

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