Power does NOT equal torque/time.
Torque is just a type of force. There is no unit to describe force/time because it has no meaning. I could put 10 ft-lbs on a lug nut until the next ice age, and I STILL would not have done ANY work (and thus produced no power) UNLESS AND UNTIL there was some movement (distance) involved. I would have to actually TWIST the lug nut, not just put torque on it, to do any work.
OK, one more time, with feeling:
Work = force x distance = torque (in ft-lbs) x distance (in revolutions)
Power = Work / Time = force x distance / time = torque x revolutions / time
After pulling some weeds in the flower garden (and getting rained out) and thinking about what you wrote, I see what you're saying.
Looking at James Watt's original definition of a horsepower, which is
1 horsepower = 33,000 lb*ft/min.
Basically, he said that one horsepower was the ability to lift 33,000 pounds one foot in one minute.
33,000 lb*ft/min is an equation that acts on a free body in a linear fashion, a body that is allowed to move. It's not uncommon to have physics problems to operate on a free body. What we want is an eqation that acts on a shaft. The equation for power in a rotational motion is P = T*w where P is power, T is torque and w is angular velocity as defined by w = d(theta)/dt where d(theta) is the angular displacement. Sorry, I'm not looking up the ascii characters for Greek.
So, torqueing a lugnut and not moving it nets zero angular displacement thus driving the horsepower to zero.
In a previous post, you wrote this:
(work is force applied OVER A DISTANCE).
That is true of work applied to a body that can move linearly. With rotation, we have no distance. We do have angular displacement though.
When we talk about torque as pertaining to engines, we assume there is angular displacement of the crankshaft, otherwise we need to start the engine.
Hope I explained it in a way you can understand and sorry I jumped the gun on my previous posts. I had to think about it. Good question.
edit: For clarification, Watt defined a horsepower as it pertains to linear motion. You crank on a lugnut in a rotational motion. A little different equation, but the same idea.