Red and blue runners stand opposite each other on a 400 meter long track. Each side, A,B,C and D is 100 meters long. There are therefore 200 meters between them.

 

Red runs at 12.7 km/h and Blue runs at 11.3 km/h

.

Question:

Where on the field does Red run catch up with Blue?

 

It must be noted with Side length+Number of meters,

e.g. B77.42 (2 decimal places, please)

We need to find out where Red catches up with Blue on a 400-meter track. Since they are running towards each other, the sum of their speeds will determine how fast the distance between them closes.

### Step-by-step solution:

1. **Convert the speeds from km/h to m/s:**

   - Red's speed: \( 12.7 \, \text{km/h} = \frac{12.7 \times 1000}{3600} \, \text{m/s} = 3.5278 \, \text{m/s} \)
   - Blue's speed: \( 11.3 \, \text{km/h} = \frac{11.3 \times 1000}{3600} \, \text{m/s} = 3.1389 \, \text{m/s} \)

2. **Relative speed (since they run towards each other):**

   \( \text{Relative speed} = 3.5278 + 3.1389 = 6.6667 \, \text{m/s} \)

3. **Initial distance between them:**

   The initial distance between them is 200 meters.

4. **Time to meet:**

   Time for them to meet \( t = \frac{\text{distance}}{\text{relative speed}} = \frac{200}{6.6667} = 30 \, \text{seconds} \).

5. **Distance Red covers in that time:**

   In 30 seconds, Red will cover \( d = 3.5278 \times 30 = 105.83 \, \text{meters} \).

6. **Final location on the track:**

   Red starts at point A. Since the total perimeter is 400 meters, we need to locate 105.83 meters from Red's starting position:

   - From point A, Red runs 100 meters to point B.
   - From point B, Red will run an additional \( 105.83 - 100 = 5.83 \, \text{meters} \) on side B.

So, Red catches up with Blue at **B5.83**.

### Conclusion:

Red catches up with Blue at **B5.83**.

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Would you like more details or have any questions?

Here are five related questions for further understanding:

1. How long does it take for Red to complete the full track at their given speed?
2. If Blue increases their speed by 2 km/h, how would the catch-up point change?
3. What if the track is not circular but rectangular; how would that affect the result?
4. How would the situation change if both runners ran in the same direction?
5. What would happen if the initial distance between the runners was reduced?

**Tip:** When dealing with problems involving relative speeds, focus on how fast the distance between the objects changes.

Red and blue runners stand opposite each other on a 400 meter long track. Each side, A, B, C, and D is 100 meters long. There are therefore 200 meters between them. Red runs at 12.7 km/h and Blue runs at 11.3 km/h. Where on the field does Red catch up with Blue? It must be noted with Side length+Number of meters, e.g. B77.42 (2 decimal places, please)

Discover how to calculate where Red catches up with Blue on a 400-meter track using relative speed and unit conversion. The problem involves calculating the distance covered by both runners and understanding relative speed. Suitable for students in Grades 8-10.

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