Hi, could you help me please
Question: A tortoise can run with a speed of 0.12 m/s and a hare can run 20 times as fast. in a race, they both start at the same time, but the hare stops to rest for 2.0 minutes. The tortoise wins by a shell (25cm).
A.How long does the race takes?
B. What is the length of race?
Thank you so much for your help.
hello from the future :)
tortoise= .12 m/s
hare= .12 x 20= 2.4m/s
rest= 2.0 minutes= 120 seconds
part A
0.12 t = (2.4)(t-120 seconds)-.25
solve for t=
for part B
use part A's answer and multiply by the tortoise's speed.
96 minutes?
691.8 meter?
Of course! I'd be happy to help you with your question.
To find out how long the race takes, we need to determine the time it takes for the tortoise to cover the distance, as the hare stops to rest.
Let's first calculate the speed of the hare. We know that the hare can run 20 times as fast as the tortoise, so the hare's speed would be 20 * 0.12 m/s = 2.4 m/s.
Now, let's calculate the distance the tortoise travels. Since the tortoise wins the race by a shell (25cm), we can convert this into meters by dividing by 100: 25cm / 100 = 0.25m.
The tortoise travels this distance at a speed of 0.12 m/s, so we can divide the distance by the speed to find out the time it takes for the tortoise to complete the race. The formula for time is: time = distance / speed.
For the tortoise: time = 0.25m / 0.12 m/s = 2.08 seconds.
Now, let's calculate the distance the hare travels before stopping. To determine this, we need to calculate the hare's running time. The hare runs at a speed of 2.4 m/s, and the time he runs without stopping is the race time minus the rest time.
The rest time is given as 2.0 minutes. To convert this to seconds, we multiply by 60: 2.0 min * 60 s/min = 120 seconds.
So the running time of the hare is the total race time (which we'll call "T") minus the rest time.
Now, the hare covers distance at a speed of 2.4 m/s, so we can write an equation for the distance covered by the hare: distance = speed * time.
For the hare: distance = 2.4 m/s * (T - 120 seconds).
Since we know the tortoise covers a distance of 0.25m, and the hare covers distance at a different pace, we can set up an equation to find T:
0.25m = 2.4 m/s * (T - 120 seconds).
Now, we can solve this equation to find the value of T, which will give us the total race time.