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The problem is asking how long it will take before Priya and Tyler run into each other after Tyler has started walking back home, assuming both leave at the same time and walk at the same rate.

Here’s a breakdown of the situation:

1. **Tyler's distance from school**: 
   - Tyler is 1 mile from the school and takes 20 minutes to walk there.
   
2. **Priya's distance from school**: 
   - Priya lives 0.25 miles farther from school than Tyler. So, Priya is 1 + 0.25 = 1.25 miles away from school.
   - Priya and Tyler walk at the same speed, so she will take 20 minutes to walk 1 mile, and 5 more minutes to walk 0.25 miles, for a total of 25 minutes to get to the school.

3. **What happens**:
   - Tyler starts walking toward the school to retrieve his math book.
   - Priya walks to school to meet Tyler on his way back home.

### To solve:
- Tyler and Priya both leave at the same time. 
- Tyler walks 1 mile to school, taking 20 minutes.
- After 20 minutes, Tyler begins walking back toward home.
- During this time, Priya has been walking toward the school from her house, which is 1.25 miles away.
  
The point of the problem is to determine how long it will take before they meet.

Let's solve it step-by-step.

We need to set up a relative distance equation since both Priya and Tyler are walking toward each other at the same rate, starting from different points. Priya has walked part of her journey while Tyler is walking back.

Let's calculate it mathematically!It will take 2.5 minutes after Tyler starts walking back from the school for Priya and Tyler to run into each other.

Thus, they will meet 22.5 minutes after they both left their houses. 

Let me know if you want further details or have any questions!

Here are five related questions to extend your understanding:
1. What if Priya walked at a slower speed than Tyler? How would that affect when they meet?
2. How much distance will Priya have covered by the time she meets Tyler?
3. If Tyler took longer to retrieve his book, how would that affect the meeting time?
4. How far from Tyler's house will they be when they meet?
5. How would the solution change if Tyler's house was farther from school?

**Tip**: When two objects move toward each other at the same speed, you can treat their relative speed as the sum of their individual speeds to simplify calculations.

Tyler and Priya are neighbors and both live on the same street as their school. Tyler's house is closer to the school and it usually takes them 20 minutes to walk 1 mile to school. Priya’s house is 0.25 miles from Tyler’s, as shown in the image. Tyler forgot their math book in their locker, so they text Priya to see if she will walk with them to school to retrieve the book. Priya tells Tyler to start walking to school and she will meet them when they are on their way back home from the school. If Priya and Tyler leave at the same time and we assume Tyler grabs their book at the school and starts back home without losing any time, how long will it take before Priya runs into Tyler? Assume Priya and Tyler walk at the same rate and take the same path to and from school.

Solve a relative motion problem where Tyler and Priya are walking toward each other at the same speed. Discover how to calculate the time it takes for them to meet, assuming Priya's house is farther from school than Tyler's. This problem explores distance, speed, and time concepts.

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