Cai is going to drive from his house to City A without stopping. Cai plans to drive at a speed of 30 miles per hour, and after driving for 4 hours, he will be 120 miles away from City A. Write an equation for D, commaD, in terms of t, commat, representing Cai's distance from City A tt hours after leaving his house.

To create the equation representing Cai's distance from City A, we can start by analyzing the information given:

1. Cai drives at a constant speed of 30 miles per hour.
2. After driving for 4 hours, Cai is 120 miles away from City A.

Let:
- \( D(t) \) represent Cai's distance from City A at time \( t \) (in hours) after leaving his house.
- \( t \) is the number of hours Cai has been driving.

Since Cai is driving at a constant speed, the relationship between his distance from City A and time can be expressed as a linear equation. We need two pieces of information to form the equation:
- Initial distance from City A: When \( t = 0 \), Cai is farther from City A, but we don't know that exact distance.
- Distance after 4 hours: When \( t = 4 \), Cai is 120 miles away from City A.

Step 1: General form of the equation is \( D(t) = D_0 - 30t \), where:
- \( D_0 \) is the initial distance from City A,
- \( 30t \) is the distance Cai covers after driving for \( t \) hours at 30 miles per hour.

Step 2: We know that when \( t = 4 \), \( D(4) = 120 \). Substituting these values into the equation:
\[
D(4) = D_0 - 30(4) = 120
\]
\[
D_0 - 120 = 120
\]
\[
D_0 = 240
\]

Step 3: The final equation for Cai's distance from City A at any time \( t \) is:
\[
D(t) = 240 - 30t
\]

This equation shows that as time increases, Cai's distance from City A decreases by 30 miles per hour.

Would you like more details or have any questions?

Here are five related questions:
1. How far is Cai from City A after 2 hours of driving?
2. How long will it take Cai to reach City A if he maintains this speed?
3. What is the interpretation of the constant 240 in the equation?
4. If Cai reduces his speed to 25 miles per hour, how would the equation change?
5. How would you solve for the time \( t \) when Cai is 50 miles away from City A?

**Tip**: Always check that the units in a word problem are consistent when setting up equations.

Cai is going to drive from his house to City A without stopping. Cai plans to drive at a speed of 30 miles per hour, and after driving for 4 hours, he will be 120 miles away from City A. Write an equation for D, in terms of t, representing Cai's distance from City A t hours after leaving his house.

Learn how to write a linear equation for distance using the distance-speed-time relationship. This example involves a driver traveling at 30 miles per hour and calculating the distance from City A after 4 hours. Suitable for students in Grades 6-8.

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