You do not have to wait 40 minutes at all... Try it out. Take a unit of infantry (as they are often those that suffers the most) and run it until it has lost 3 bars (takes a good time I would say). Then wait. The wait isn't much longer than the time, if at all, you run around.

So if it takes you 5 minutes to walk to the foot of the hill, then wait for another 5. 5 minutes is not much.