A speedy tortoise can run at 0.09 m/s, and a hare can run 20 times as fast. In a race, they start at the same time, but the hare stops to rest for 2.4 min, so the tortoise wins by a shell

(20 cm).
How long does the race take?
Answer in units of s

What is the length of the race?
Answer in units of m

DO NOT ROUND AT ALL

To find the length of the race, we first need to calculate how long it takes for the hare to rest. We are given that the hare rests for 2.4 minutes, but we need to convert it to seconds for consistency.

1 minute = 60 seconds

So, the hare rests for 2.4 minutes * 60 seconds/minute = 144 seconds.

Next, we can calculate the time it takes for the tortoise to finish the race. We know that the hare runs 20 times faster than the tortoise, so the hare's speed is 0.09 m/s * 20 = 1.8 m/s.

Let's assume the length of the race is represented by 'd' meters.

Since both the hare and the tortoise start at the same time, the tortoise takes the same amount of time to reach the finish line as the hare. We can represent the time it takes for the tortoise to finish the race as 't' seconds.

We can set up an equation to represent the relationship between distance, speed, and time:

d = 0.09 m/s * t

The length of the race is d meters.

To find the time it takes for the tortoise to finish the race, we need to rearrange the equation:

t = d / 0.09

Now we can substitute t into the equation for the hare's speed:

t = d / 0.09
1.8 = d / 0.09

Now we can solve for d by cross-multiplying:

1.8 * 0.09 = d
0.162 = d

The length of the race is 0.162 meters.

To find the total time it takes for the race, we need to consider the hare's resting time. The hare stops for 144 seconds, so the total time it takes for the race is:

Total time = t + 144

Substituting our earlier equation for t, we get:

Total time = d / 0.09 + 144
Total time = 0.162 / 0.09 + 144

Now we can calculate the total time:

Total time = 1.8 + 144
Total time = 145.8 seconds

Therefore, the race takes 145.8 seconds and the length of the race is 0.162 meters.