Hello,

I've attached a rough sketch of the situation.

. Thus

First calculate the distances:

is the distance which is travelled by canoe.

is the distance to jog.

Now use the formula to calculate the time needed:

This is a function of t in x. Calculate the first derivative:

. To get the minimum t'(x) = 0:

. Square the equation and multiply by (1+x²). You'll get

The only possible result is x = 0.75

Plug in this value in t(x) and you get the minimum time: 0.86666 ... = 13/15 hours = 52 minutes.

EB