Titus took `30` minutes to walk `2` miles at a constant rate. 

`d` is the distance Titus walks, in miles.

`t` is the time it takes Titus to walk, in minutes.



Write two different equations to represent the relationship between `d` and `t`.

To represent the relationship between the distance `d` and time `t`, we can use two different approaches based on the information given. Since Titus walks at a constant rate, we can use the concept of rate (speed) to form these equations.

### 1. Using the formula for constant speed:

The general formula for speed (rate) is:

\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]

Given that Titus walks 2 miles in 30 minutes, his speed is:

\[
\text{Speed} = \frac{2 \text{ miles}}{30 \text{ minutes}} = \frac{1}{15} \text{ miles per minute}
\]

So, the first equation representing the relationship between distance \(d\) and time \(t\) is:

\[
d = \frac{1}{15}t
\]

### 2. Rearranging the speed equation:

We can also rearrange the same relationship in a different form to express time \(t\) in terms of distance \(d\). From the speed equation:

\[
t = \frac{d}{\frac{1}{15}} = 15d
\]

Thus, the second equation is:

\[
t = 15d
\]

### Summary of the two equations:
1. \( d = \frac{1}{15}t \)
2. \( t = 15d \)

These two equations show the relationship between distance and time for Titus walking at a constant rate.

---

Would you like more details on any of the steps? Here are some follow-up questions:

1. How can we find the time taken to walk any distance using the second equation?
2. What is the distance walked if Titus walks for 45 minutes?
3. How would we graph the relationship between distance and time?
4. What does the slope of the graph of \(d = \frac{1}{15}t\) represent?
5. If Titus walks for 1 hour, how far does he walk?

**Tip**: In word problems, identifying the rate is key to setting up equations for distance, time, and speed.

Titus took `30` minutes to walk `2` miles at a constant rate. `d` is the distance Titus walks, in miles. `t` is the time it takes Titus to walk, in minutes. Write two different equations to represent the relationship between `d` and `t`.

Explore how to represent the relationship between distance and time when walking at a constant speed. This problem involves writing two equations, using the rate formula, and understanding linear equations. Suitable for students in Grades 6-8.

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