Question

Kellie and her sister Ashley are training for a race. Kellie ran 8 miles in 72 minutes. Ashley ran 12 miles in 102 minutes. please show work
(a) What is Kellie’s minute-per-mile pace?


(b) How far did Ashley run in 34 minutes?


(c) What was the difference in Kellie and Ashley’s times after they ran 4 miles?

Answer 1

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:

$p=\frac{t}{d}$

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:

$p=\frac{72 min}{8 mi}=9 min/mi$

b)

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

$v=\frac{d}{t}$

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

$v=\frac{12}{102}=\frac{2}{17} mi/min$

The distance covered in a time t is given by

$d=vt$

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

$d=(\frac{2}{17})\cdot 34 =4 mi$

c)

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

$t_a=34 min$

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)

$p=9 \frac{min}{mi}$

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

$t=pd$

And substituting, we find:

$t=9\cdot 4 = 36 min$

So, the difference in time is:

$\Delta t = 36 min - 34 min = 2 min$

So Kellie takes 2 minutes more to run 4 miles.