The tortoise and the hare are in a race of 1000m distance. The tortoise travels the entire race at a speed of 2.0 m/s while the rabbit runs the first 200 m @ 2.0 m/s. Then he stops to take nap for 1.3 hrs and awakens to finish the last 800m with an average speed of 3.0 m/s. Who wins the race & by how much? *need helping setting it up*

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For the tortoise, we know:

- Distance = 1000m
- Speed = 2.0 m/s

Therefore, we can use the formula:

time = distance / speed

to find the time it takes for the tortoise to complete the race:

time = 1000m / 2.0 m/s = 500 seconds

For the hare, we will need to break it down into two parts:

- First 200m @ 2.0 m/s
- Last 800m with an average speed of 3.0 m/s

We can use the same formula to find the time it takes for the hare to run the first 200m:

time = distance / speed = 200m / 2.0 m/s = 100 seconds

Next, we need to find the time it takes for the hare to run the last 800m with an average speed of 3.0 m/s. We know that the total time the hare takes for this part of the race is 1.3 hours + the time it takes to run the distance:

time = 1.3 hours + (800m / 3.0 m/s)

We need to convert 1.3 hours to seconds, so:

1.3 hours = 1.3 x 60 x 60 = 4680 seconds

time = 4680 seconds + 266.7 seconds = 4946.7 seconds

Now, we can add up the times for both parts of the hare's race to find her total time:

total time = 100 seconds + 4946.7 seconds = 5046.7 seconds

So who wins the race? The tortoise takes 500 seconds while the hare takes 5046.7 seconds. Therefore, the tortoise wins the race by a margin of:

margin = hare's time - tortoise's time = 5046.7 seconds - 500 seconds = 4546.7 seconds

Therefore, the tortoise wins the race by a margin of 4546.7 seconds!

To determine who wins the race and by how much, we need to calculate the time taken by both the tortoise and the hare to finish the race.

First, let's calculate the time taken by the tortoise to complete the 1000 m race. We can use the formula: time = distance / speed.

Distance (d) = 1000 m
Speed of the tortoise (vt) = 2.0 m/s

Time taken by the tortoise (tt) = d / vt = 1000 m / 2.0 m/s = 500 seconds

Now, let's calculate the time taken by the hare to complete the race. The hare runs the first 200 m @ 2.0 m/s, then takes a nap for 1.3 hrs (which is 1.3 x 3600 = 4680 seconds), and finally runs the last 800 m with an average speed of 3.0 m/s.

Time taken for the first 200 m (t1) = distance / speed = 200 m / 2.0 m/s = 100 seconds

Time taken for the last 800 m (t2) = distance / speed = 800 m / 3.0 m/s = 266.67 seconds

Total time taken by the hare (th) = t1 + 4680 s + t2 = 100 s + 4680 s + 266.67 s = 5046.67 seconds

Now that we have the time taken by both the tortoise (500 seconds) and the hare (5046.67 seconds), we can determine who wins the race and by how much.

Since the tortoise finishes the race in less time than the hare, the tortoise wins the race. The time difference between the tortoise and the hare is:

Time difference (td) = time taken by the hare - time taken by the tortoise
td = 5046.67 s - 500 s = 4546.67 seconds

Therefore, the tortoise wins the race by a time difference of 4546.67 seconds.

To determine who wins the race and by how much, we need to compare the time it takes for the tortoise to finish the race with the time it takes for the hare to finish the race.

First, let's calculate the time taken by the tortoise to complete the race:

Distance = Speed × Time

Time = Distance / Speed

The distance is 1000m, and the tortoise's speed is 2.0 m/s.

Time taken by the tortoise = 1000m / 2.0 m/s = 500 seconds

Next, let's calculate the time taken by the hare to complete the race.

The hare runs the first 200m at a speed of 2.0 m/s and then stops for a nap for 1.3 hours. After awakening, the hare finishes the final 800m at an average speed of 3.0 m/s.

Time taken for the first 200m = Distance / Speed = 200m / 2.0 m/s = 100 seconds

Time taken for the last 800m = Distance / Speed = 800m / 3.0 m/s = 266.67 seconds

Time taken for the nap = 1.3 hours × 60 minutes/hour × 60 seconds/minute = 4680 seconds

Total time taken by the hare = Time taken for the first 200m + Time taken for the nap + Time taken for the last 800m
= 100 seconds + 4680 seconds + 266.67 seconds
= 5046.67 seconds

Now, we can compare the times taken by the tortoise and the hare to determine the winner:

Since the tortoise takes 500 seconds to complete the race and the hare takes 5046.67 seconds, we can conclude that the tortoise wins the race.

To find out by how much the tortoise wins, we can subtract the time taken by the hare from the time taken by the tortoise:

Time difference = Time taken by the tortoise - Time taken by the hare
= 500 seconds - 5046.67 seconds
= -4546.67 seconds

The negative sign indicates that the tortoise finishes the race earlier than the hare by 4546.67 seconds. In other words, the tortoise wins the race by approximately 4546.67 seconds or 75 minutes and 46.67 seconds.