An elite Tour de France cyclist can maintain an output power of 450 W during a sustained climb. At this output power, how long would it take an 88 kg cyclist (including the mass of his bike) to climb the famed 1100-m-high Alpe d'Huez mountain stage?

T = 35' 08"

Explanation:

By definition, the power is the rate of change of energy, with respect to time:

       

ΔE, in this case, must be equal to the change in the gravitational potential energy during the climb (neglecting friction), as follows:

       

From (1) and (2), being P= 450 W, we can solve for Δt, as follows:

       

Converting seconds to minutes, we get: Δt = 35' 08"