a) 9 minutes/mile
b) 4 miles
c) 2 minutes
Step-by-step explanation:
a)
The minute-per-mile pace is equivalent to the reciprocal of the speed, so it can be calculated as:
![p=\frac{t}{d}](https://tex.z-dn.net/?f=p%3D%5Cfrac%7Bt%7D%7Bd%7D)
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:
![p=\frac{72 min}{8 mi}=9 min/mi](https://tex.z-dn.net/?f=p%3D%5Cfrac%7B72%20min%7D%7B8%20mi%7D%3D9%20min%2Fmi)
b)
First of all, we have to calculate Ashley's speed. This is given by
![v=\frac{d}{t}](https://tex.z-dn.net/?f=v%3D%5Cfrac%7Bd%7D%7Bt%7D)
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
![v=\frac{12}{102}=\frac{2}{17} mi/min](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B12%7D%7B102%7D%3D%5Cfrac%7B2%7D%7B17%7D%20mi%2Fmin)
The distance covered in a time t is given by
![d=vt](https://tex.z-dn.net/?f=d%3Dvt)
Therefore, for t = 34 min, the distance covered is:
![d=(\frac{2}{17})\cdot 34 =4 mi](https://tex.z-dn.net/?f=d%3D%28%5Cfrac%7B2%7D%7B17%7D%29%5Ccdot%2034%20%3D4%20mi)
c)
We already know from part b) that the time taken for Ashley to cover 4 miles is
![t_a=34 min](https://tex.z-dn.net/?f=t_a%3D34%20min)
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)
![p=9 \frac{min}{mi}](https://tex.z-dn.net/?f=p%3D9%20%5Cfrac%7Bmin%7D%7Bmi%7D)
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
![t=pd](https://tex.z-dn.net/?f=t%3Dpd)
And substituting, we find:
![t=9\cdot 4 = 36 min](https://tex.z-dn.net/?f=t%3D9%5Ccdot%204%20%3D%2036%20min)
So, the difference in time is:
![\Delta t = 36 min - 34 min = 2 min](https://tex.z-dn.net/?f=%5CDelta%20t%20%3D%2036%20min%20-%2034%20min%20%3D%202%20min)
So Kellie takes 2 minutes more to run 4 miles.