Question

A car passes through a tollbooth at 8:00 A.M. and begins traveling east at an average speed of the same tollbooth an hour later and begins traveling east at an average speed of 60 miles per hour. a. Write an equation for each car that relates the number of hours x since 8:00 A.M. to the distance in miles y the car has traveled. Explain what the slope of each equation represents. b. Graph the system of equations on the coordinate plane. c. If neither car stops, at what time will the second car catch up to the first car? Explain how you determine your answer.

Answer 1

The distance traveled by both cars is an illustration of a linear function.

• The equations of both cars are $\mathbf{y=60x - 540}$ and $\mathbf{y=45x - 360}$
• Both cars meet at 12:00pm

Car A

Speed = 45 miles per hour

So, the coordinates of car A are:

$\mathbf{(x,y) = (8,0) (9, 45) (10, 90) ....}$

Car B

Speed = 60 miles per hour

So, the coordinates of car B are:

$\mathbf{(x,y) = (9, 0) (10, 60) (11, 120) ....}$

(a) The equation of both cars

Car A

This is calculated as:

$\mathbf{y = mx+ b}$

Where m represents slope/speed.

So, m = 45

This gives

$\mathbf{y = 45x + b}$

y = 0, when x = 8.

So, we have:

$\mathbf{0= 45\times 8 + b}$

$\mathbf{0= 360 + b}$

Solve for b

$\mathbf{b=- 360}$

So, the equation of car A is:

$\mathbf{y=45x - 360}$

Car B

This is calculated as:

$\mathbf{y = mx+ b}$

Where m represents slope/speed.

So, m = 60

This gives

$\mathbf{y = 60x + b}$

y = 0, when x = 9.

So, we have:

$\mathbf{0= 60\times 9 + b}$

$\mathbf{0= 540 + b}$

Solve for b

$\mathbf{b=- 540}$

So, the equation of car B is:

$\mathbf{y=60x - 540}$

(b) The graphs

See attachment

(c) The time which both cars meet

We have:

$\mathbf{y=60x - 540}$ and $\mathbf{y=45x - 360}$

Equate both

$\mathbf{60x - 540=45x - 360}$

Collect like terms

$\mathbf{60x - 45x = 540- 360}$

$\mathbf{15x = 180}$

Divide both sides by 15

$\mathbf{x = 12}$

This means that both cars meet at 12:00pm

Read more about linear functions at:

brainly.com/question/20286983