A tortoise can run with a speed of 0.13 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 4.0 minutes. The tortoise wins by a shell (35 cm).

(a) How long does the race take?
(b) What is the length of the race?

To determine the answers, we will calculate the time taken by both the tortoise and the hare and compare them.

Let's start with part (a) - the duration of the race:

1. First, we need to calculate the time it takes for the hare to complete the race. We know that the hare runs at a speed 20 times faster than the tortoise, so its speed is 0.13 m/s * 20 = 2.6 m/s.

2. With this information, we can calculate the time it takes for the hare to complete the race distance. As we don't know the distance, we will denote it as "d." Using the formula: time = distance / speed, we can write: time_hare = d / 2.6.

3. The tortoise wins the race by a shell, which is 35 cm or 0.35 m. So, the distance covered by the hare is d + 0.35 m.

4. The tortoise's speed is given as 0.13 m/s. We can use the same formula as before to calculate the time it takes for the tortoise to complete the race distance: time_tortoise = (d + 0.35) / 0.13.

5. Since both the hare and tortoise start at the same time, the race duration will be the sum of the time taken by both: race_duration = time_hare + time_tortoise.

Next, let's move on to part (b) - the length of the race:

1. From the information given in the problem, we know that the tortoise wins by a shell, which is 35 cm or 0.35 m. Thus, the length of the race will be the same as the distance covered by the hare plus this additional distance: race_length = d + 0.35.

Now, let's plug in the values and calculate the answers:

(a) Calculation of the race duration:
time_hare = d / 2.6
time_tortoise = (d + 0.35) / 0.13
race_duration = time_hare + time_tortoise

(b) Calculation of the race length:
race_length = d + 0.35

To find specific numerical values, we would need additional information, such as the distance covered by the hare (d). With this information, we can plug it into the equations to find the answers.

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