Question

Marcus can drive his boat 24 miles down the river in 2 hours but takes 3 hours to return upstream. Find the rate of the boat in still water and the rate of the current.

Answer 1

Answer:

speed of boat as

$v_b = 10 mph$

river speed is given as

$v_r = 2 mph$

Explanation:

When boat is moving down stream then in that case net resultant speed of the boat is given as

since the boat and river is in same direction so we will have

$v_1 = v_r + v_b$

Now when boat moves upstream then in that case the net speed of the boat is opposite to the speed of the river

so here we have

$v_2 = v_b - v_r$

as we know when boat is in downstream then in that case it covers 24 miles in 2 hours

$v_1 = \frac{24}{2} = 12 mph$

also when it moves in upstream then it covers same distance in 3 hours of time

$v_2 = \frac{24}{3} = 8 mph$

$v_b + v_r = 12 mph$

$v_b - v_r = 8 mph$

so we have speed of boat as

$v_b = 10 mph$

river speed is given as

$v_r = 2 mph$

Answer 2

The rate of the boat in still water is 10 mph

The rate of the current is 2 mph

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:

distance covered = d = 24 miles

time for driving down the river = td = 2 hours

time for driving up the river = tu = 3 hours

Unknown:

velocity of the boat in still water = vs = ?

velocity of the current = vc = ?

Solution:

When Marcus drive his boat down the river , the velocity of the boat is in the same direction to the velocity of the current.

$v_s + v_c = \frac{d}{t_d}$

$v_s + v_c = \frac{24}{2}$

$v_s + v_c = 12$

$v_s = 12 - v_c$ → Equation 1

When Marcus drive his boat up the river , the velocity of the boat is in the opposite direction to the velocity of the current.

$v_s - v_c = \frac{d}{t_d}$

$v_s - v_c = \frac{24}{3}$

$v_s - v_c = 8$

$12 - v_c - v_c = 8$ ← Equation 1

$12 - 2v_c = 8$

$2v_c = 12 - 8$

$2v_c = 4$

$v_c = 4 \div 2$

$\large {\boxed {v_c = 2 ~ mph} }$

$v_s = 12 - v_c$

$v_s = 12 - 2$

$\large {\boxed {v_s = 10 ~ mph} }$

Learn more

• Velocity of Runner : https://brainly.com/question/3813437

• Kinetic Energy : https://brainly.com/question/692781

• Acceleration : https://brainly.com/question/2283922

• The Speed of Car : https://brainly.com/question/568302

Answer details

Grade: High School

Subject: Physics

Chapter: Kinematics

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