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.