Optimal route consisting of rowing then walking Problem
You're in a boat on point A in the water, and you need to get to point B on land. Your rowing speed is 3km/h, and your walking speed 5km/h.
See figure:

Find the route that takes the least amount of time.
My idea
I started by marking an arbitrary route:

From here, I figure the total time is going to be $$T = \frac{R}{3\mathrm{km/h}} + \frac{W}{5\mathrm{km/h}}$$
Since this is a function of two variables, I'm stuck.
A general idea is to express $W$ in terms of $R$ to make it single-variable, and then apply the usual optimization tactics (with derivatives), but I'm having a hard time finding such an expression.
Any help appreciated!
EDIT - Alternative solution?
Since the distance from A to the right angle (RA) is traveled 3/5 times as fast as the distance between RA and B, could I just scale the former up?
That way, I get A-RA being a distance of $6\cdot\frac53 = 10\mathrm{km}$, which makes the hypotenuse $\sqrt{181}$ the shortest distance between A and B. And since we scaled it up, we can consider it traversable with walking speed rather than rowing speed!
Thoughts?

You do not need to worry about the hypotenuse in the larger right triangle.
Consider the right triangle that has R as the hypotenuse. Left side of this triangle will have length $6$ and the top side will have length $(9-W)$. By the Pythagorean theorem, $R^{2} = 36+(9-W)^2$.  
Solving for R and inserting in your original equation yields $T= \frac{1}{3} \sqrt{36+(9-W)^{2}} + \frac{1}{5} W$. This function is strictly convex, so you can simply minimize it by solving $\frac{d\ T}{d\ W}=0$ (the 'usual optimization tactics').
Regarding your alternative solution, I am unsure what you are arguing. The shortest distance between the points A and B will always be the line connecting them. As you have shown in your drawing, $|AB|=3\sqrt{13} \ne\sqrt{181}$.
