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

Explanation:

a)

The minute-per-mile pace is equivalent to the reciprocal of the speed, so it can be calculated as:

`p=(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=(72 min)/(8 mi)=9 min/mi`

b)

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

`v=(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=(12)/(102)=(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=((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 (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.