A speedy tortoise can run at 0.08 m/s, and a hare can run 16 times as fast. In a race, they start at the same time, but the hare stops to rest for 2 min, so the tortoise wins by a shells(20cm). How long does the race take? Answer in units of s

To determine the duration of the race, we first need to calculate the relative speed between the tortoise and the hare, since they start at the same time. Given that the tortoise's speed is 0.08 m/s, we can find the hare's speed by multiplying it by 16.

Hare's speed = 0.08 m/s * 16 = 1.28 m/s

Now, let's calculate the distance covered by the tortoise during the time the hare rests. Since the hare stops to rest for 2 minutes, we need to convert this time into seconds, which gives us 120 seconds. The tortoise's speed remains constant throughout the race, so we can easily calculate the distance covered:

Distance covered by tortoise = Speed * Time
Distance = 0.08 m/s * 120 s = 9.6 meters

Since the tortoise wins by a shells (20 cm), or 0.2 meters, we can calculate the total distance of the race:

Total distance of the race = Distance covered by tortoise + Winning margin
Total distance = 9.6 m + 0.2 m = 9.8 meters

Finally, we can determine the duration of the race by dividing the total distance by the relative speed between the tortoise and the hare:

Time = Distance / Speed
Time = 9.8 meters / 1.28 m/s = 7.65625 seconds

Therefore, the duration of the race is approximately 7.66 seconds.