$\mathrm{}\mathrm{}$ A weightlifter has a basal metabolic rate of $80\mathrm{.}0$ W$.$ As he is working out, his metabolic rate increases by $650\mathrm{.}0$ W$.$

$($a$)$ How many hours does it take him to work off a $450\mathrm{.}0$ Calories bagel if stays in bed? $$

$($b$)$ How long does it take him if he is working out?

(c)  Calculate the amount of mechanical energy to lift a $120\mathrm{.}0$ kg barbell $2\mathrm{.}00$ m high? 

$($d$)$ He then drops the barbell and lifts it repeatedly. How many times per minute must he repeat the process to do the amount of mechanical work equivalent to his metabolic rate increase of $650\mathrm{.}0$ W during the exercise?  

 $($e$)$ Could he do repetitions at the rate found in part$($d$)$ at the given metabolic level? Explain.