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?

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:

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.

astronomers is your final answer! : )

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.