Question

this question has two parts. first, answer part a. then, answer part b.
part a
some boats were traveling up and down a river. a satellite recorded the movements of several boats.
a motor boat traveled -3.4 miles per hour for 0.75 hours. how far did it go?
miles
a tugboat traveled -1.5 miles in 0.3 hours. what was its velocity?
miles per hour
part b
complete the statements about what you think negative distances and velocities could mean in this situation.
positive distances could mean distances in the positive direction and negative distances mean distances in the select choice direction. positive velocities could mean it was moving in the positive direction and negative velocities mean it was moving in the select choice direction.
select choice
same
opposite

Explanation:

Part A

First Question (Motor Boat Distance)

Step1: Recall distance formula

The formula for distance \( d \) is \( d = v \times t \), where \( v \) is velocity and \( t \) is time.

Step2: Substitute values

Here, \( v=-3.4 \) miles per hour and \( t = 0.75 \) hours. So \( d=(-3.4)\times0.75 \).

Step3: Calculate the product

\( (-3.4)\times0.75=-2.55 \) miles.

Second Question (Tugboat Velocity)

Step1: Recall velocity formula

The formula for velocity \( v \) is \( v=\frac{d}{t} \), where \( d \) is distance and \( t \) is time.

Step2: Substitute values

Here, \( d = - 1.5 \) miles and \( t=0.3 \) hours. So \( v=\frac{-1.5}{0.3} \).

Step3: Calculate the quotient

\( \frac{-1.5}{0.3}=-5 \) miles per hour.

Part B

In the context of boats moving up and down a river, we can define a positive direction (for example, downstream) and a negative direction (upstream). So negative distances would mean distances in the opposite direction of the positive direction, and negative velocities would mean the boat is moving in the opposite direction of the positive velocity direction (i.e., upstream if positive is downstream). So both blanks should be filled with "opposite".

Answer:

Part A

• Motor boat distance: \(-2.55\) miles
• Tugboat velocity: \(-5\) miles per hour

Part B

• First blank: opposite
• Second blank: opposite