Let's say the cost per mile with Brian driving is x dollars. Then, based on the given information, we know that the total cost after driving 5 miles is $30, which includes the $10 base fee. So:
Total cost = base fee + cost per mile x distance
$30 = $10 + x(5)
Simplifying the equation:
$20 = 5x
Dividing both sides by 5:
x = $4
Therefore, Brian charges $4 per mile.