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 11 mph 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 time he spent bicycling at 11 mph be x and the time spent bicycling at 15 mph be y, then
x + y = 60 . . . (1)
7x + 11.75y = 600 . . . (2)
(2) x 7 => 7x + 7y = 420 . . . (3)
(2) - (3) => 4.75y = 180
y = 180 / 4.75 = 38
x = 60 - 38 = 22

Therefore, he should bicycle 22 minutes at 11 mph and 38 minutes at 15 mph.

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