Elizabeth is going to drive from her house to City A without stopping. Elizabeth's house is 120 miles from City A and she plans to drive at a speed of 30 miles per hour. Make a table of values and then write an equation for D, commaD, in terms of t, commat, representing Elizabeth's distance from City A tt hours after leaving her house.

Your answer has been placed on the table in column 2 row 5 with a green checkmark

Number of Hours Driving	Distance Remaining to City A (Miles)

00	120, check mark120✓120

11	90, check mark90✓90

22	60, check mark60✓60

33	30, check mark30✓30

Answer

Attempt 1 out of 2

D, equalsD=


Let's first look at the pattern for Elizabeth's drive and then derive the equation for her distance from City A after driving for \( t \) hours.

Given:
- Elizabeth's house is 120 miles from City A.
- She drives at 30 miles per hour.

**Table of values**:

| Number of Hours Driving \( t \) | Distance Remaining to City A \( D \) (Miles) |
|-------------------------------|-------------------------------------------|
| 0                             | 120                                       |
| 1                             | 90                                        |
| 2                             | 60                                        |
| 3                             | 30                                        |
| 4                             | 0                                         |

**Deriving the equation**:
The distance remaining \( D \) decreases by 30 miles for every hour of driving. Therefore, the distance \( D \) after \( t \) hours of driving is given by the initial distance minus the distance covered, which is \( 30t \).

So, the equation for \( D \) in terms of \( t \) is:

\[
D = 120 - 30t
\]

### Answer:
\[
D = 120 - 30t
\]

Would you like any further details or clarifications?

### 5 Relative Questions:
1. How long will it take Elizabeth to reach City A?
2. If Elizabeth's speed were 40 miles per hour, what would the equation for \( D \) be?
3. How far from City A is Elizabeth after 2.5 hours of driving?
4. If Elizabeth drives for 4.5 hours, how much distance would she have covered?
5. What happens to the equation if Elizabeth makes a stop for a break?

### Tip:
When writing equations to model real-life situations, always check the units to ensure consistency (e.g., miles per hour, miles, hours).

Elizabeth is going to drive from her house to City A without stopping. Elizabeth's house is 120 miles from City A and she plans to drive at a speed of 30 miles per hour. Make a table of values and then write an equation for D, representing Elizabeth's distance from City A t hours after leaving her house.

Understand how to calculate Elizabeth's distance from City A after driving at 30 miles per hour. This linear equation problem explores the distance-speed-time relationship, with step-by-step solutions and a value table. Ideal for students in Grades 6-8.

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