Question

Carrie and brent leave home at the same time. carrie drives due east at a rate of 30 mph, while brent drives due south at a rate of 60 mph. how far apart are they (to the nearest mile) after 4 hours.

Answer 1

They are 268 miles far apart after 4 hours

Further explanation

Acceleration is rate of change of velocity.

$\large {\boxed {a = \frac{v - u}{t} } }$

$\large {\boxed {d = \frac{v + u}{2}~t } }$

a = acceleration ( m/s² )

v = final velocity ( m/s )

u = initial velocity ( m/s )

t = time taken ( s )

d = distance ( m )

Let us now tackle the problem !

Given :

v₁ = 30 mph due east

v₂ = 60 mph due south

t = 4 hours

Unknown :

displacement = d = ?

Solution :

$d_1 = v_1 \times t$

$d_1 = 30 ~ mph \times 4 ~ h$

$d_1 = \boxed {120 ~ miles}$

$d_2 = v_2 \times t$

$d_2 = 60 ~ mph \times 4 ~ h$

$d_2 = \boxed {240 ~ miles}$

$d^2 = (d_1)^2 + (d_2)^2$

$d^2 = 120^2 + 240^2$

$d^2 = 72000$

$d = \sqrt{72000}$

$d = 120\sqrt{5} ~ miles$

$d \approx \boxed {268 ~ miles}$

Conclusion :

They are 268 miles far apart after 4 hours

Learn more

• Velocity of Runner : brainly.com/question/3813437
• Kinetic Energy : brainly.com/question/692781
• Acceleration : brainly.com/question/2283922
• The Speed of Car : brainly.com/question/568302

Answer details

Grade: High School

Subject: Physics

Chapter: Kinematics

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Speed , Time , Rate

Answer 2

The Carrie and Brent are $\boxed{268{\text{ miles}}}$ apart from each other after 4 hours.

Further explanation:

The relationship between speed, distance and time can be expressed as follows,

$\boxed{{\text{Speed}} = \frac{{{\text{Distance}}}}{{{\text{Time}}}}}$

Given:

Carrie drives due east at a rate of $30{\text{ miles/hour}}.$

Brent drives due south at a rate of $60{\text{ miles/hour}}.$

Explanation:

Consider the distance covered by the Carrie as ${d_c}.$

The distance covered by the Carrie can be obtained as follows,

$\begin{aligned}30&= \frac{{{d_c}}}{4}\\{d_c} &= 4 \times 30\\{d_c}&= 120{\text{ miles}}\\\end{aligned}$

Consider the distance covered by the Brent as ${d_b}.$

The distance covered by the Brent can be obtained as follows,

$\begin{aligned}60&= \frac{{{d_b}}}{4} \hfill\\{d_b} &= 4 \times 60 \hfill\\{d_b} &= 240{\text{ miles}} \hfill\\\end{aligned}$

The Carrie and Brent are $\boxed{268{\text{ miles}}}$ apart from each other after 4 hours.

Learn more:

1. Learn more about inverse of the function brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Speed

Keywords: Carrie, Brent, leave, same time, time, leave home, Carrie drives, east, rate, 30 mph, south, drive to south, 4 hours, 60 mph, far, apart,