Since Gunton is due north of Kipton and Lawton is due east, Gunton-Kipton-Lawton form a right angle. Since we don’t know the speed we can’t yet directly equate the given times and the given distances. Let’s say we are travelling at ‘s’ miles per minute. We can create the following diagram:

We can use the law of cosines to give an expression for cos(a) and cos(90-a) in terms of s:

Cos(a) = (15^2+(78s)^2–(102s-15)^2)/(2*15*78s)

Cos(a) = (17-24s)/13

Cos(90-a) = (16^2+(78s)^2–(82s-16)^2)/(2*16*78s)

Cos(90-a) = (41-10s)/39

But, cos(90-a) is also expressible as sin(a), and (sin(a))^2+(cos(a))^2=1

(51-72s)^2+(41-10s)^2 = 39^2

5284s^2-8164s+2761=0

s can be 1/2 or 2761/2642

If we use this second figure and plot the resulting distances, Torton would be way to the north-west, not generally north-east as stated, so the speed is 1/2 mile/minute or 30mph. The distance between Kipton and Torton is therefore 39 miles.