Question

A paddock on level ground is 2km long and 1km wide. If a farmer walks from one corner to the opposite corner along the fences in 40 minutes, how long will it take him walks across the diagonal?

Answer 1

This is easily imagined as a right triangle, which generally means trigonometry!

We want to find the hypotenuse,

Given,

`b = 2*10^3"m"`, and `a = 1*10^3"m"`

`t = 40"min" * (60"s")/"min" approx 2400"s"`

Hence,

`theta_"A" = tan^-1(a/b) approx 26.6°`, and by extension,

`Deltax = c = a/(sin theta_"A") approx 2.24*10^3"m"`

Now, let's derive his average speed,

`bars = (Deltad)/t approx (1.25"m")/"s"`

Which we can approximate to be his velocity due to your lack of data, and solve for the answer. Hence,

`=> t = (Deltad)/(bars) approx 1.8*10^3"s" approx 30"min"`

is the time it takes for the farmer to complete his trip: more efficient!