Chapter 8.8, Problem 42PPS

(a)

To determine

Write the equation for Emilee’s trip where $y$ is the total distance from the park after $x$ hours.

Answer to Problem 42PPS

The equation for Emilee’s trip where $y$ is the total distance from the park after $x$ hours is

  $y=225-70x$ .

Explanation of Solution

Given:

Emilee’s Total Distance $=225$ miles and Driving Miles $=70$

Justyne’s Total Distance $=200$ miles and Driving Miles $=65$

The equation for Emilee’s trip where $y$ is the total distance from the park after $x$ hours,

As Speed $=70$ Mph.

Distance $=225$ miles.

  $y=225-70x;x=$ Number of Hours

  $y$ is total distance after $x$ hours.

Conclusion:

Thus The equation for Emilee’s trip where $y$ is the total distance from the park after $x$ hoursis

  $y=225-70x$ .

(b)

To determine

Write an equation for Justyne’s trip where $y$ is the total distance from the park after $x$ hours.

Answer to Problem 42PPS

The equation for Justyne’s trip where $y$ is the total distance from the park after $x$ hours, is

  $y=200-65x$

Explanation of Solution

Given:

Emilee’s Total Distance $=225$ miles and Driving Miles $=70$

Justyne’s Total Distance $=200$ miles and Driving Miles $=65$

Justyne’s trip where $y$ is the total distance from the park after $x$ hours.

Justyne’s Total Distance $=200$ miles and Driving Miles $=65$

  $y=200-65x;x=$ Hours of trip.

  $y$ is total distance after $x$ hours.

Conclusion:

The equation for Justyne’s trip where $y$ is the total distance from the park after $x$ hours, is

  $y=200-65x$

(c)

To determine

Graph the two equations on the same coordinate plane.

Answer to Problem 42PPS

The Graph is

Explanation of Solution

Given:

Emilee’s Equation $y=225-70x$

Justyne’s Equation $y=200-65x$

  

Red: Emilee’s Equation

Blue:Justyne’s Equation

Conclusion:

The Graph is drawn as,

  

(d)

To determine

Explain the overlap of Emilee’s and Justyne’s trip.

Answer to Problem 42PPS

They don’t overlap at any point.

Explanation of Solution

Given:

Emilee’s Total Distance $=225$ miles and Driving Miles $=70$

Justyne’s Total Distance $=200$ miles and Driving Miles $=65$

Emilee:

According to the problem, Emilee starts at 225 miles from the park, this is an initial condition, and so it’s gone be the independent term. She travels at a rate of 70 miles per hour, this is gone be the coefficient of the variables, because ratio refers to the slope.

So Emilee’s expression would be,

  $y=-70x+225$

Justyne’s:

With the same procedure for the Emilee. She starts at 200 miles from the part and she travels with a ratio of 65 miles per hour. So the liner expression would be,

  $y=-65x+200$

With the help of graph, you will get more understanding that they don’t overlap at any point. This means that they don’t overlap during the travel.

Conclusion:

Thus, theydon’t overlap at any point.