The domain of the function is the set of all the values of x that would allow the function to have real values. Since the radicand is x - 3, the value of x cannot be less than 3 because that would make the value of sqrt (x - 3) an imaginary number. Thus, the domain should be all numbers GREATER than or equal to 3.
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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