A tortoise can run with a speed of 10.1 cm/s, and a hare can run 19.4 times as fast. In a race, they both start at the same time, but the hare stops to rest for 122 seconds. The tortoise wins by a shell (20.8 cm).
How long does the race take?
What is the length of the race?
tortoise= 10.1 t
hare= 195.94(t-122)
tortoise - hare= 10.1t - 195.94t + 23904.68 = 20.8
Solve for t
23883.88 = 185.84 t
t = 128.5185 s
tortoise t= (10.1)(128.5185)= 129.036 cm
A tortoise and a hare are having a 1.00km race. The tortoise runs the race at a constant speed of 2.30 cm/s. The hare moves at an average speed of 1.50 m/s for 10.0 minutes and then decides to take a nap. After waking up from the nap, the hare recognizes that the tortoise is about to cross the finish line and immediately accelerates from rest with a constant acceleration of 0.500 m/s2 for the remaining distance of the race. If the tortoise wins by a hair (pun intended), then what is the time (in hours) that the hare napped?
To find the time it takes for the race to be completed, we can use the formula: time = distance/speed.
The tortoise wins by a shell, which means it completes the race length while the hare is still 20.8 cm behind. Therefore, the distance the tortoise needs to cover is the length of the race minus 20.8 cm.
Given that the tortoise's speed is 10.1 cm/s, we can now find the time it takes for the tortoise to complete the race.
time_tortoise = (race length - 20.8 cm) / tortoise's speed
Now let's find the length of the race. Since the hare is 19.4 times faster than the tortoise, we can use the hare's speed to determine the distance covered by the hare in the same amount of time it took the tortoise to complete the race.
distance_hare = hare's speed * time_tortoise
Now, we need to subtract the distance covered by the hare after resting for 122 seconds.
distance_hare -= hare's speed * 122 seconds
Since the tortoise wins the race by 20.8 cm, the distance covered by the hare after resting should be 20.8 cm shorter than the length of the race.
distance_hare = race length - 20.8 cm
Now we can equate both expressions for the distance covered by the hare.
race length - 20.8 cm = hare's speed * time_tortoise - hare's speed * 122 seconds
We can now solve this equation to find the length of the race.