Question

Two athletes in an 800 metre race take 104 seconds and 108 seconds respectively to complete the race. Assuming each athlete is running at a constant speed, calculate the distance between them when the faster athlete is at the finishing line.

Answer 1

To determine the distance between the two athletes when the faster athlete finishes the 800-meter race, we first need to calculate their respective speeds.

For the faster athlete:
- Distance: \( 800 \) meters
- Time: \( 104 \) seconds
- Speed: \(\frac{800 \text{ meters}}{104 \text{ seconds}} = \frac{200}{26} \approx 7.692 \text{ meters/second} \)

For the slower athlete:
- Distance: \( 800 \) meters
- Time: \( 108 \) seconds
- Speed: \(\frac{800 \text{ meters}}{108 \text{ seconds}} \approx 7.407 \text{ meters/second} \)

Now, we need to find out how far the slower athlete has run when the faster athlete finishes the race.

Time taken by the faster athlete to finish the race: \( 104 \) seconds.

Using the slower athlete's speed, we find the distance covered by the slower athlete in \( 104 \) seconds:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
\[ \text{Distance} = 7.407 \times 104 \approx 770.33 \text{ meters} \]

Therefore, the distance between the two athletes when the faster athlete finishes the race is:
\[ 800 \text{ meters} - 770.33 \text{ meters} \approx 29.67 \text{ meters} \]

So, the distance between them is approximately \(29.67\) meters.