Your classmate is starting a new fitness program. he is planning to ride his bicycle 60 minutes every day. he burns 7 calories per minute bicycling at 11mph and 11.75 calories per minute bicycling at 15 mph. how long should he bicycle at each speed to burn 600 calories per hour?

Let the number of minutes he  spent bicycling at 11mph be x and the number of minutes spent bicycling at 15mph be y, then

x + y = 60 . . . (1)
7x + 11.75y = 600 . . . (2)

(1) x 7 => 7x + 7y = 420 . . . (3)
(2) - (3) => 4.75y = 180
y = 180 / 4.75 ≈ 38 minutes

From (1), x + 38 = 60
x = 60 - 38 = 22 minutes

Therefore, he will spend 22 minutes bicycling at 11 mph and 38 minutes bicycling at 15 mph.