Question

lesson 3 - homework
a plane flew at a constant speed between new york and san diego. it took the plane 5 hours to fly 2,400 miles.
a. how far does the plane fly in one hour?
480 miles
b. how far would the plane fly in t hours at this speed?
c. if d represents the distance that the plane flies at this speed for t hours, write an equation that relates t and d.

Explanation:

Part A

Step1: Recall the formula for speed

Speed is calculated as the distance traveled divided by the time taken. The formula is \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \).

Step2: Identify the given values

The distance between New York and San Diego is \( 2400 \) miles, and the time taken by the plane is \( 5 \) hours.

Step3: Calculate the speed

Substitute the given values into the speed formula: \( \text{Speed} = \frac{2400}{5} = 480 \) miles per hour.

Step1: Recall the formula for distance

The formula for distance is \( \text{Distance} = \text{Speed} \times \text{Time} \). We already found the speed of the plane in part A, which is \( 480 \) miles per hour.

Step2: Express the distance in terms of time \( t \)

Let \( d \) be the distance flown in \( t \) hours. Using the distance formula, we substitute the speed (\( 480 \) mph) and time (\( t \) hours) into the formula: \( d = 480 \times t \), or simply \( d = 480t \).

Step1: Define the variables

We are given that \( d \) represents the distance the plane flies at this speed for \( t \) hours. From part B, we know the relationship between distance, speed, and time.

Step2: Write the equation

Using the formula \( \text{Distance} = \text{Speed} \times \text{Time} \), and since the speed is \( 480 \) mph (from part A), the equation relating \( t \) (time in hours) and \( d \) (distance in miles) is \( d = 480t \). We can also solve for \( t \) in terms of \( d \) by dividing both sides by \( 480 \), giving \( t = \frac{d}{480} \). But the most direct relationship from the problem's context (expressing \( d \) in terms of \( t \)) is \( d = 480t \).

Answer:

The plane flies \( 480 \) miles in one hour.

Part B