Your classmate is starting a new fitness program. he is planning to ride his bicycle 60 minutes every day. he burns 8 calories per minute bicycling at 11 mph and 12.75 calories per minute bicycling at 15 mph. how long should he bicycle at each speed to burn 575 calories?
Let x be the number of minutes he should bicycle at 11 mph.
Then 60 - x is the number of minutes he should bicycle at 15 mph.
So, the total number of calories burned at 11 mph is 8x.
And the total number of calories burned at 15 mph is 12.75(60 - x).
The total number of calories burned is 8x + 12.75(60 - x) = 575.
Simplifying the equation, we get 8x + 765 - 12.75x = 575.
Combining like terms, we get -4.75x + 765 = 575.
Subtracting 765 from both sides, we get -4.75x = -190.
Dividing both sides by -4.75, we get x = 40.
So, he should bicycle for 40 minutes at 11 mph and 60 - 40 = 20 minutes at 15 mph. Answer: \boxed{40, 20}.