Heat Engines and Efficiency

$3.$ A heat engine idealized as operating on the Carnot cycle is supplied with heat at the boiling point of water $(212F),$ and it rejects heat at the freezing point of water $(32F.$ If the engine produces $100$ hp of mechanical work,

$($a$)$ Determine the efficiency of the engine.

$($b$)$ Calculate in units of Btu the amount of heat that must be supplied to the engine each hour.