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The problem describes a coach using a 50-meter tape that is actually 50.20 meters long. The task is to measure a 200-meter straightaway course accurately, despite the tape being slightly longer than expected.

### Analysis:

1. **Actual Tape Length:** The tape is 50.20 meters long, but it is labeled as 50 meters.
2. **Required Course Length:** The course needs to be exactly 200 meters.

### Steps:

1. **Conversion Factor:** 
   Since the tape is longer than expected, each measured length is larger than it should be. The conversion factor between the tape’s actual length and the desired length is:
   \[
   \text{Conversion Factor} = \frac{50 \text{ meters}}{50.20 \text{ meters}} = 0.996
   \]
   This means each "50 meters" marked with the tape is only \(0.996\) of the actual 50.20 meters.

2. **Number of Tape Lengths:**
   The course is 200 meters long. If the tape were exactly 50 meters long, it would take 4 measurements to complete the course:
   \[
   \text{Number of Measurements} = \frac{200 \text{ meters}}{50 \text{ meters}} = 4 \text{ measurements}
   \]

3. **Adjusted Measurements:**
   Each measurement needs to be multiplied by the conversion factor to account for the tape's extra length:
   \[
   \text{Adjusted Length per Measurement} = 50 \times 0.996 = 49.80 \text{ meters}
   \]
   So, for each segment measured, the coach should measure 49.80 meters instead of using the full 50.20 meters of the tape.

### Conclusion:

The coach should measure four segments of 49.80 meters each to lay out the correct 200-meter course.

Would you like further clarification or details on this problem? Here are five related questions to explore:

1. How would the measurement change if the tape were shorter than 50 meters?
2. What is the impact of using a longer tape on the overall measurement process?
3. How could the coach verify the accuracy of the course after laying it out?
4. What would happen if a curved track were being measured instead of a straightaway?
5. How would this problem change if the coach needed a 400-meter course?

**Tip:** Always check the calibration of measuring tools before use, especially for precise measurements like in sports or engineering.

A track and field coach wishes to lay out for his team a 200-m straightaway course. If he uses a 50-m tape known to be 50.20m long, determine the measurements to be made so that the course will have the correct length.

Learn how to accurately measure a 200-m straightaway course using a 50-m tape that is slightly longer than expected. This problem involves correcting the measurement using a conversion factor, suitable for high school students in Grades 9-12.

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