Jai is going to drive from his house to City A without stopping. Jai's house is 300 miles from City A and after driving for 2 hours, he will be 240 miles away from City A. Write an equation for D, comma*D*, in terms of t, comma*t*, representing Jai's distance from City A t*t* hours after leaving his house.

To represent Jai's distance from City A, \( D \), as a function of time, \( t \), we can model this situation using a linear equation.

### Step 1: Determine Jai's initial distance
At \( t = 0 \) (the moment Jai starts driving), he is 300 miles away from City A. So, the initial distance \( D_0 \) is 300 miles.

### Step 2: Find the rate of change (speed)
We know that after driving for 2 hours, Jai will be 240 miles away from City A. This means that in 2 hours, he covers:

\[
\text{Distance covered} = 300 - 240 = 60 \text{ miles}
\]

Thus, Jai's speed is:

\[
\text{Speed} = \frac{60 \text{ miles}}{2 \text{ hours}} = 30 \text{ miles per hour}
\]

This means Jai is decreasing his distance from City A by 30 miles each hour.

### Step 3: Write the equation
The general form of the equation for distance is:

\[
D(t) = D_0 - \text{(rate)} \times t
\]

Substituting the known values:

\[
D(t) = 300 - 30t
\]

Thus, the equation for Jai's distance \( D \) (in miles) from City A as a function of time \( t \) (in hours) is:

\[
D(t) = 300 - 30t
\]

This equation tells us that Jai's distance from City A decreases by 30 miles for each hour he drives.

Would you like more details or have any questions about this?

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Here are 5 relative questions to expand on this:

1. How long will it take Jai to reach City A at his current speed?
2. What would be the distance equation if City A were 400 miles away instead of 300 miles?
3. How would the equation change if Jai were driving at 40 miles per hour?
4. What if Jai had already been driving for 1 hour before the problem began—how would that change the equation?
5. How would you graph the equation \( D(t) = 300 - 30t \), and what would the slope represent?

**Tip:** Linear equations like this one model many real-world situations, such as distance-time relationships, where the rate of change (slope) is constant.

Jai is going to drive from his house to City A without stopping. Jai's house is 300 miles from City A and after driving for 2 hours, he will be 240 miles away from City A. Write an equation for D, *D*, in terms of t, *t*, representing Jai's distance from City A t hours after leaving his house.

This problem models Jai's distance from City A using a linear equation. Given that Jai's house is 300 miles from City A, and after 2 hours he is 240 miles away, the solution walks through creating the equation D(t) = 300 - 30t. Suitable for students in Grades 6-8, this example illustrates basic distance-time relationships and linear equations.

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