John and Bill are running at constant speeds of 4 m/s and 7 m/s respectively on a 250 meter circular track. If John is 25 meters behind Bill, how many minutes will it take for the two runners to meet on the track?

Let's break down the problem step by step.

### Given:
- John runs at a speed of 4 m/s.
- Bill runs at a speed of 7 m/s.
- They are running on a 250-meter circular track.
- John is 25 meters behind Bill.

### Approach:

1. **Relative Speed**: 
   Since both are running in the same direction, their relative speed is the difference between their speeds:
   \[
   \text{Relative Speed} = 7 \, \text{m/s} - 4 \, \text{m/s} = 3 \, \text{m/s}
   \]
   This means Bill is getting ahead of John by 3 meters every second.

2. **Distance to be Covered**:
   John is initially 25 meters behind Bill. On the circular track, the distance John needs to "catch up" is this 25-meter gap.

3. **Time Calculation**:
   The time it takes for John to catch up to Bill can be calculated using the formula:
   \[
   \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}}
   \]
   Substituting the values:
   \[
   \text{Time} = \frac{25 \, \text{meters}}{3 \, \text{m/s}} = 8.33 \, \text{seconds}
   \]

4. **Convert to Minutes**:
   To convert seconds to minutes:
   \[
   \text{Time in minutes} = \frac{8.33}{60} = 0.139 \, \text{minutes}
   \]

### Conclusion:
It will take John approximately **0.139 minutes** (or about **8.33 seconds**) to meet Bill on the track.

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### 5 Related Questions:
1. What if John was 50 meters behind Bill initially?
2. How would the time change if both runners increased their speed by 2 m/s?
3. How long would it take for John to lap Bill on the circular track?
4. If they were running in opposite directions, how long would it take them to meet?
5. What is the total distance each runner covers until they meet?

### Tip:
When working with relative motion, always consider the speed difference when both objects are moving in the same direction.

John and Bill are running at constant speeds of 4 m/s and 7 m/s respectively on a 250 meter circular track. If John is 25 meters behind Bill, how many minutes will it take for the two runners to meet on the track?

In this problem, John and Bill are running on a 250-meter circular track at speeds of 4 m/s and 7 m/s respectively. John is initially 25 meters behind Bill. Learn how to calculate the time it takes for them to meet using relative speed and time formulas. Suitable for students in Grades 8-10.

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