Power & Stair Climbing: Reviewing Old Homework

[Rentheil]

Homework Statement

Assume that the maximum rate at which your body can expend energy is 250W. Assuming a 20 percent efficiency for the conversion of chemical energy to mechanical energy, estimate how quickly you can run up four flights of stairs with each flight 3.5m high.
Teacher told us to assume 50kg.

Homework Equations

$$Power = \frac{dW}{dt}$$
$$Efficiency = \frac{Work out}{Work In}$$

The Attempt at a Solution

$$\frac{dW}{dt} = \frac{20}{100} x 250$$

$$\frac{mgh}{t} = \frac{20}{100} x 250 x 4$$

$$t = \frac{mgh}{200} = \frac{(50)(9.81)(14)}{200} = 34.3s$$

The answer nearly matches the books, which did not give a mass to use. My problem is i can't remember where the 4 came from. I know its four flights of stairs but i wouldn't think to worry about that if i have the total height. I was thinking the Power would be constant instead of 1/4 for each set of stairs, which appears to be what i did, 50W per 3.5m. Otherwise it would be something like mgh/50. Any insight would be helpful. Thanks.

 

[xcvxcvvc]

i think the four is an error

 

[Redbelly98]

I agree the 4 should not be there. Also, a healthy human body is capable of expending much higher power than 250W.