Question

a car traveled 180 miles at a constant rate.
a. complete the table to show the rate at which the car was traveling if it completed the same distance in each number of hours.

travel time (hours)	rate of travel (miles per hour)
4.5
3
2.25

b. which equation would make it easy to find the rate at which the car was traveling in miles per hour ( r ), if it traveled for ( t ) hours? equation

Explanation:

Step1: Recall the formula for rate

The formula relating distance \( d \), rate \( r \), and time \( t \) is \( d = r\times t \), so we can solve for rate \( r \) as \( r=\frac{d}{t} \). Here, the distance \( d = 180 \) miles.

Step2: Calculate rate for 5 hours

For \( t = 5 \) hours, substitute into \( r=\frac{d}{t} \). So \( r=\frac{180}{5}=36 \) miles per hour.

Step3: Calculate rate for 4.5 hours

For \( t = 4.5 \) hours, \( r=\frac{180}{4.5} \). We can rewrite \( 4.5=\frac{9}{2} \), so \( r = 180\div\frac{9}{2}=180\times\frac{2}{9} = 40 \) miles per hour.

Step4: Calculate rate for 3 hours

For \( t = 3 \) hours, \( r=\frac{180}{3}=60 \) miles per hour.

Step5: Calculate rate for 2.25 hours

For \( t = 2.25 \) hours, \( 2.25=\frac{9}{4} \), so \( r = 180\div\frac{9}{4}=180\times\frac{4}{9}=80 \) miles per hour.

Step6: Find the equation for part b

From \( d = r\times t \) and \( d = 180 \), we can solve for \( r \) to get \( r=\frac{180}{t} \) or \( r\times t=180 \) (either form is acceptable, but \( r=\frac{180}{t} \) is more direct for finding \( r \) given \( t \)).

Answer:

Part a Table:

Travel Time (hours)	Rate of Travel (miles per hour)
4.5	40
3	60
2.25	80

Part b Equation:

\( r=\frac{180}{t} \) (or \( rt = 180 \))