A hare and a tortoise compete in a race over a course 1.20 km long. The tortoise crawls straight and steadily at its maximum speed of 0.540 m/s toward the finish line. The hare runs at its maximum speed of 9.00 m/s toward the goal for 0.800 km and then stops to taunt the tortoise. How close to the goal can the hare let the tortoise approach before resuming the race, which the tortoise wins in a photo finish? Assume that, when moving, both animals move steadily at their respective maximum speeds.

Question

A hare and a tortoise compete in a race over a course 1.20 km long. The tortoise crawls straight and steadily at its maximum speed of 0.540 m/s toward the finish line. The hare runs at its maximum speed of 9.00 m/s toward the goal for 0.800 km and then stops to taunt the tortoise. How close to the goal can the hare let the tortoise approach before resuming the race, which the tortoise wins in a photo finish? Assume that, when moving, both animals move steadily at their respective maximum speeds.

Answer 1

Let X be the distance before the finish line that the tortoise can get before the hare resumes running. The hare has 400 m to go, and will require 400/9 = 44.4 s to finish. The tortoise requires

X/0.54 seconds to finish.
For a close "photo finish",
44.4 s = X/0.54 m/s
X = 24 m

Answer 2

To determine how close the hare can let the tortoise approach before resuming the race, we can calculate the time it takes for the hare to reach the point where it would let the tortoise catch up.

First, we need to calculate the time it takes for the hare to cover 0.800 km at a speed of 9.00 m/s:

Time taken by the hare = Distance / Speed
Time taken by the hare = 0.800 km / (9.00 m/s)
Time taken by the hare = 0.800 km * (1000 m/km) / (9.00 m/s)
Time taken by the hare = 88.89 s

Now, let's determine how far the tortoise can crawl in 88.89 seconds at its speed of 0.540 m/s:

Distance covered by the tortoise = Speed * Time
Distance covered by the tortoise = 0.540 m/s * 88.89 s
Distance covered by the tortoise = 48.00 m

Therefore, the hare can let the tortoise approach as close as 48.00 meters before resuming the race.

Answer 3

To solve this problem, we need to determine the distance at which the hare can let the tortoise approach before resuming the race.

Let's calculate the time it takes for the hare to run 0.800 km (800 meters) since the tortoise will be crawling the whole time.

Time taken by the hare to run 0.800 km:
Distance = Speed × Time
800 meters = 9.00 m/s × Time
Time = 800 meters / 9.00 m/s
Time ≈ 88.89 seconds

Now let's find out how far the tortoise can crawl in 88.89 seconds.

Distance crawled by the tortoise in 88.89 seconds:
Distance = Speed × Time
Distance = 0.540 m/s × 88.89 seconds
Distance ≈ 48.15 meters

So, the hare can let the tortoise approach up to approximately 48.15 meters from the finish line before resuming the race.