Jeremiah left the college traveling 8 mph. Then, 3 hours later, Francesca left traveling the same direction at 20 mph. How long until Francesca catches up with Jeremiah?

Let \( t \) represent the time (in hours) it takes for Francesca to catch up to Jeremiah after she starts her journey.

### Step 1: Distance Formula
The general formula for distance is:
\[
\text{Distance} = \text{Rate} \times \text{Time}
\]
- Jeremiah’s speed: 8 mph.
- Francesca’s speed: 20 mph.

Since Francesca leaves 3 hours after Jeremiah, during the time \( t \), Jeremiah will have been traveling for \( t + 3 \) hours.

### Step 2: Set Up the Equation
At the time Francesca catches up, they will have traveled the same distance. So, the distances traveled by both should be equal:
\[
\text{Jeremiah's Distance} = \text{Francesca's Distance}
\]
\[
8(t + 3) = 20t
\]

### Step 3: Solve for \( t \)
1. Distribute on the left side:
   \[
   8t + 24 = 20t
   \]

2. Subtract \( 8t \) from both sides:
   \[
   24 = 12t
   \]

3. Divide both sides by 12:
   \[
   t = 2
   \]

### Step 4: Conclusion
Francesca will catch up with Jeremiah in 2 hours after she starts her journey.

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Would you like further details on this solution, or do you have any questions?

Here are 5 related questions:
1. What is the total distance traveled by each person when Francesca catches up?
2. How much longer had Jeremiah been traveling when Francesca caught up?
3. If Francesca traveled at 15 mph instead, how long would it take to catch up?
4. What if Jeremiah started at 10 mph instead of 8 mph, how would the time change?
5. How would this problem change if both traveled in opposite directions?

**Tip:** Always relate the total distance traveled by both individuals to set up your equation.

Learn how to solve a distance problem where Francesca, traveling at 20 mph, catches up to Jeremiah, who is traveling at 8 mph. The solution uses the distance formula and linear equations, ideal for Grades 6-8 students.

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