Question

a motor boat traveled 18 miles down a river in 2 hours but took 4.5 hours to return upstream. Find the rate of the motor boat in still water and the rate of the current. (Round to the nearest tenth).

Answer 1

The rate of the motor boat in still water and the rate of the current is 6.5 mph and 2.5 mph respectively

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 traveled = d = 18 miles

time taken for travelling downstream = td = 2 hours

time taken for travelling upstream = tu = 4.5 hours

Unknown:

velocity of motor boat = vb = ?

velocity of current = vc = ?

Solution:

When motor boat traveled downstream , the velocity of motor boat was in the same direction to the velocity of current :

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

$v_b + v_c = \frac{18}{2}$

$\boxed {v_b + v_c = 9}$ → Equation 1

When motor boat traveled upstream , the velocity of motor boat was in the opposite direction to the velocity of current :

$v_b - v_c = \frac{d}{t_u}$

$v_b - v_c = \frac{18}{4.5}$

$\boxed {v_b - v_c = 4}$ → Equation 2

Next , Equation 1 and Equation 2 could be solved by using Elimination Method.

$(v_b + v_c) - (v_b - v_c) = 9 - 4$

$2v_c = 5$

$v_c = 5 \div 2$

$v_c = \boxed {2.5 ~ \text{mph}}$

$v_b + v_c = 9$

$v_b + 2.5 = 9$

$v_b = 9 - 2.5$

$v_b = \boxed {6.5 ~ \text{mph}}$

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

Answer 2

Answer:

• rate of the boat in still water = 6.5 miles / hour

• rate of the current = 2.5 miles / hour.

Explanation:

1) Name the two variables:

• c: rate of the current

• b: rate of the boat in still water:

With that, the net rates of the boat down the river and upstrean are:

• down the river: b + c

• upstream: b - c

2) Now set the equations for the distance as a function of the times and the rates:

• distance = rate × time

• downstream: 18 miles = (b + c) × 2 hours

• upstream: 18 miles = (b - c) × 4.5 hours

3) Set the system of equations:

• 18 = 2(b + c) ⇒ 9 = b + c . .  . Equation (1)

• 18 = 4.5 (b - c) ⇒ 4 = b - c . . . Equation (2)

4) Solve the system by elimination:

• Add equations (1) and (2): 9 + 4 = 2b

• Divide both sides by 2: 13/2 = b

• Simplify: b = 6.5

• Replace b with 6.5 in equation (2) and solve:

       4 = 6.5 - c ⇒ c = 6.5 - 4 = 2.5

5) Results:

• b = rate of the boat in still water = 6.5 miles / hour

• c = rate of the current = 2.5 miles / hour.