The distance covered in the first hour is the integral from x to x+1 of 1/t dt. The antiderivative of 1/t is ln(t) so the total distance covered in the first hour is ln((x+1)/x).

By the same reasoning the distance covered in the second hour in ln((x+2)/(x+1)).

Using the fact that it the plow traveled twice as
far in the first hour as the second: ln((x+1)/x) = ln((x+2)/(x+1))^{2}

Exp both sides and you have (x+1)/x = ((x+2)/(x+1))^{2}.

Solving for x you get x=(5^{1/2}-1)/2, which is the number
of hours that elapsed between the time it started snowing and the snow plow
left.

This problem was taken from the *Actuarial Review*, although
I heard it somewhere else before.

Michael Shackleford, A.S.A.