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*
2 answers
dont know
No worries, let me help you set it up!
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!
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!
1 answer