What is the speed of the runner on each type of track?

Steps to Solve

1. Convert Time to Seconds

First, convert the time taken for each track from minutes to seconds.

Use the conversion: $$ \text{Time (seconds)} = \text{Time (minutes)} \times 60 $$

For example, for Grass: $$ 6.2 \text{ minutes} \times 60 = 372 \text{ seconds} $$

2. Calculate Speed for Each Track

Next, calculate the speed for each track using the formula: $$ \text{Speed (m/s)} = \frac{\text{Distance (meters)}}{\text{Time (seconds)}} $$

For Grass: $$ \text{Speed} = \frac{1000}{372} \approx 2.688 \text{ m/s} $$

3. Repeat for Remaining Tracks

Continue this calculation for Gravel, Concrete, and Turf.

For Gravel: $$ 5.7 \text{ minutes} \times 60 = 342 \text{ seconds} $$ $$ \text{Speed} = \frac{1000}{342} \approx 2.924 \text{ m/s} $$

For Concrete: $$ 5.0 \text{ minutes} \times 60 = 300 \text{ seconds} $$ $$ \text{Speed} = \frac{1000}{300} \approx 3.333 \text{ m/s} $$

For Turf: $$ 5.5 \text{ minutes} \times 60 = 330 \text{ seconds} $$ $$ \text{Speed} = \frac{1000}{330} \approx 3.030 \text{ m/s} $$

4. Summarize the Results

Finally, summarize the speeds calculated for each track type.

• Grass: $ \approx 2.688 \text{ m/s} $
• Gravel: $ \approx 2.924 \text{ m/s} $
• Concrete: $ \approx 3.333 \text{ m/s} $
• Turf: $ \approx 3.030 \text{ m/s} $