A tortoise can run with a speed of 0.10m/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 2.0min. The tortoise wins by a shell (20cm). How long does the race take? What is the length of the race?

Your school subject is Math, not college.

To determine the length of the race, we first need to find the time it takes for the hare to complete the race.

Given that the tortoise's speed is 0.10 m/s, we can calculate the hare's speed by multiplying it by 20: 0.10 m/s * 20 = 2.0 m/s.

Since the hare stops to rest for 2.0 minutes, we need to convert this time into seconds: 2.0 minutes * 60 seconds/minute = 120 seconds.

Now, we can calculate the distance the hare would have covered during this rest period by multiplying its speed by the time: 2.0 m/s * 120 s = 240 meters.

Next, we find the distance covered by the tortoise. We know that the tortoise wins by a shell, which is 20 cm. To compare the distance between the two racers, we need to express this in meters: 20 cm/100 = 0.20 meters.

Let's assume the race length is 'x' meters.

The tortoise travels 'x' meters, and the hare travels 'x + 0.20' meters (taking the shell into account).

The time it takes for both racers to complete their distances can be expressed as follows:

Time taken by the tortoise: x meters / 0.10 m/s = x/0.10 seconds
Time taken by the hare: (x + 0.20 meters) / 2.0 m/s = (x + 0.20)/2.0 seconds

Since the hare takes a rest of 120 seconds while the tortoise keeps running, the equation becomes:

(x/0.10) = (x + 0.20)/2.0 + 120

Simplifying the equation:

2(x/0.10) = (x + 0.20) + 240

Simplifying further:

20x = 10x + 20 + 240

Combining like terms:

10x = 260

Dividing both sides by 10:

x = 26

Therefore, the length of the race is 26 meters.

To find the time it takes for the race to be completed, we substitute the value of x into either the tortoise or hare's time equation.

Using the tortoise's equation:
Time taken by the tortoise: x/0.10 = 26/0.10 = 260 seconds

Thus, the race takes 260 seconds (or 4 minutes and 20 seconds) to complete.