I timed a regular shower - 6 1/4 minutes.
Not convinced that the order of washing the same numer of square inches in the same arrangement (torso, arms,legs) would make a significant difference in the timing, I opted to take a Navy shower. The whole shower took under 3 minutes. I ran the water for about 1 minute.
For someone wanting to bathe quickly, I recommend a Navy shower. It's a no brainer.