a) 9 minutes/mile
b) 4 miles
c) 2 minutes
Explanation:
a)
The minute-per-mile pace is equivalent to the reciprocal of the speed, so it can be calculated as:

where
d is the distance covered
t is the time taken to cover that distance
For Kellie in this problem, we have:
d = 8 miles (distance covered)
t = 72 minutes (time taken)
Therefore, her minute-per-mile pace is given by:

b)
First of all, we have to calculate Ashley's speed. This is given by

d is the distance covered
t is the time taken to cover that distance
For Ashley, we have
d = 12 miles (distance)
t = 102 minutes (time)
So, her speed is

The distance covered in a time t is given by

Therefore, for t = 34 min, the distance covered is:

c)
We already know from part b) that the time taken for Ashley to cover 4 miles is

Therefore now we have to find the time taken for Kellie to cover the same 4 miles.
We know that the minutes-per-mile pace of Kellie is (part a)

Here we want to find the time taken for Kellie to cover a distance of
d = 4 miles
This can be obtained with the equation

And substituting, we find:

So, the difference in time is:

So Kellie takes 2 minutes more to run 4 miles.