Your classmate is starting a new fitness program. he is planning to ride his bicycle 45 minutes every day. he burns 6 calories per minute bicycling at 11 mph and 9.75 calories per minute bicycling at 15 mph. how long should he bicycle at each speed to burn 300 calories?

he should bicycle for _ minutes at 11 mph and _ minutes at 15 mph.

Let x be the time at 11 mph, and let y be the time at 15 mph.
x + y = 45 (1)
Therefore:
y = 45 - x (2)

Now we can write the equation for the total calories required:
6x + 9.75y = 300 (3)

Plugging the value for y from equation (2) into equation (3), we get:
6x + 9,75(45 - x) = 300 (4)
which simplifies to:
-3.75x = -138.75
x = -138.75/-3.75 = 37 minutes.
The answer is 37 minutes at 11 mph and 8 minutes at 15 mph.