A tortoise can run with a velocity of 10 cm/s and hare can run 20 times as fast. In a race they start at the same time but the hare stops to rest for 2 minutes. The tortoise wins by 20 cm. What was the length of the race
Well, it seems like the tortoise had a real "slow and steady" advantage, huh? Let's do some humor-math to solve this puzzling race.
We know that the tortoise's velocity is 10 cm/s, and the hare runs 20 times as fast, meaning its velocity is 200 cm/s. Quite the difference! 🐢🐇
Now, during the hare's nap time, which lasted 2 minutes, we need to figure out how far the tortoise traveled. The tortoise runs at a speed of 10 cm/s for 2 minutes, which is a total of 10 cm/s x 120 seconds = 1200 cm. So while the hare was snoozing away, the tortoise made some great progress.
After those 2 minutes, the hare wakes up and continues racing. But, lo and behold, even with its lightning speed, the tortoise still manages to win by 20 cm. Quite impressive, Mr. Tortoise! 🎉
So if the tortoise won by 20 cm, that means the hare must have run a total of 1180 cm (1200 cm - 20 cm) before it woke up. Now, since the hare runs 20 times faster than the tortoise, we can set up an equation:
Tortoise's distance = Hare's distance / 20
1180 cm = Hare's distance / 20
To find the hare's distance, we multiply both sides of the equation by 20:
Hare's distance = 1180 cm x 20 = 23600 cm
So the hare ran a total distance of 23600 cm. Phew, that's quite a long race!
Now, adding the distance the tortoise ran during the nap time, we get:
Total distance = Tortoise's distance + Hare's distance
= 1200 cm + 23600 cm
= 24800 cm
So, the length of the race was 24800 cm. My goodness, that's one memorable race! 🚀
To find the length of the race, we need to determine the time it takes for both the tortoise and the hare to finish.
Let's consider the tortoise first. We know that the tortoise's velocity is 10 cm/s. Let's assume it takes the tortoise t seconds to finish the race. Therefore, the distance covered by the tortoise would be given by:
Distance = Velocity × Time
Distance = 10 cm/s × t
Distance = 10t cm
Now, let's consider the hare. We are given that the hare runs 20 times as fast as the tortoise, so its velocity would be 20 × 10 cm/s = 200 cm/s. However, we also need to account for the 2-minute rest period. Since 1 minute is equal to 60 seconds, the rest period is equal to 2 × 60 = 120 seconds. Therefore, the time taken by the hare to finish the race would be t + 120 seconds. The distance covered by the hare would be:
Distance = Velocity × Time
Distance = 200 cm/s × (t + 120)
Distance = 200t + 24000 cm
We are given that the tortoise wins the race by 20 cm. So, we can set up an equation using the distances covered by the tortoise and the hare:
10t = 200t + 24000 - 20
-190t = -24020
t = 126.947 seconds
Now that we know the time it took for the tortoise to finish the race, we can find the length of the race:
Distance = Velocity × Time
Distance = 10 cm/s × 126.947 s
Distance ≈ 1269.47 cm
Therefore, the length of the race is approximately 1269.47 cm.