Does Doubling Horsepower Double Elevator Speed?

[NewJersey]

An elevator is running with a 25hp motor. to double the lift speed a ____ hp motor is required.

To double the lift speed should we just times 25 by 2 and get 50hp motor. Or is there something more to this.

 

[Mindscrape]

How does power relate to speed? You aren't necessarily wrong or right, but you should be wrong or right for the correct reasoning.