High School

**Track Meet Strategy**

You are helping to coach a runner, Jorge, who is training for a track meet. Jorge will compete in the 1500-meter race against Alex, the best runner from another school. Your task is to develop a strategy to help Jorge finish the race before Alex.

**Running Data:**
- Jorge's average speed is 5.9 meters per second for distances less than 500 meters.
- Jorge's average speed is 5.5 meters per second for distances greater than 500 meters.
- Alex can finish the 1500-meter race in 4 minutes and 25 seconds.

**Track Information:**
- One lap around the track is 400 meters.
- The race involves running a total of 1500 meters.

**Question:**
How long will it take Jorge to complete the 1500-meter race at his average speed for each distance segment?

**Enter the number of seconds, rounded to the nearest tenth, in the response box:**

Seconds: [ ]

Answer :

To determine how long it will take Jorge to complete the 1500-meter race, we need to consider his average speeds for different segments of the race. According to the data provided:

  1. Jorge's speed for the first 500 meters:

    He runs at an average speed of 5.9 meters per second for distances less than 500 meters.

    The time to complete the first 500 meters can be calculated using the formula:

    [tex]\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{500 \text{ meters}}{5.9 \text{ meters/second}}[/tex]

    Calculating this gives:

    [tex]\text{Time for first 500 meters} = \frac{500}{5.9} \approx 84.7 \text{ seconds}[/tex]

  2. Jorge's speed for the remaining 1000 meters:

    For distances greater than 500 meters, his speed is 5.5 meters per second.

    The time to complete the remaining 1000 meters can be calculated as:

    [tex]\text{Time} = \frac{1000 \text{ meters}}{5.5 \text{ meters/second}}[/tex]

    Calculating this gives:

    [tex]\text{Time for remaining 1000 meters} = \frac{1000}{5.5} \approx 181.8 \text{ seconds}[/tex]

  3. Total time to complete the 1500-meter race:

    By adding the two times calculated above, we get Jorge's total race time:

    [tex]\text{Total Time} = 84.7 \text{ seconds} + 181.8 \text{ seconds}[/tex]

    This results in:

    [tex]\text{Total Time} \approx 266.5 \text{ seconds}[/tex]

Therefore, it will take Jorge approximately 266.5 seconds to complete the 1500-meter race.

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