A test car is driven a fixed distance of n miles along a straight highway. (Here n ∈ Z+.) The car travels at one mile per hour for the first mile, two miles per hour for the second mile, four miles per hour for the third mile, . . . , and 2n~l miles per hour for the nth mile.
(a) What is the car's average velocity for the first four miles?
(b) For a given value of n, what is the car's average velocity for the first n miles?
(c) Find the smallest value of n for which the car's average velocity for the first n miles exceeds 10 miles per hour.