A speedy tortoise can run at 0.14m/s, and a hare can run 15 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 shell(20cm). How long does the race take?

the run the same distance.

distancetortiose= .14*time
distancehard=15*.14(t-2)

set the distances equal, and solve for t, which is time in minutes.

To find the time it takes for the race to be completed, we can calculate the time it takes for both the tortoise and the hare to reach the finish line.

First, let's determine the distance they need to run.

Given:
Speed of the tortoise = 0.14 m/s
Speed of the hare = 15 times the speed of the tortoise = 15 * 0.14 m/s = 2.1 m/s

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

Since the tortoise wins by a shell, the difference in their distances is 20 cm, which is equal to 0.2 m.

Distance covered by the tortoise = Distance covered by the hare + 0.2 m

Using the formula: Distance = Speed * Time

(0.14 m/s) * Time taken by the tortoise = (2.1 m/s) * Time taken by the hare + 0.2 m

Now let's find the time taken by the hare to reach the finish line (before the tortoise).

Distance traveled by the hare = Speed of the hare * Time taken by the hare

Distance traveled by the hare = 2.1 m/s * Time taken by the hare

Since the hare stops to rest for 2 minutes, the time taken by the hare will be 2 minutes less than the total race time.

Time taken by the hare = Total race time - 2 minutes

Plugging this back into the equation:

(0.14 m/s) * Time taken by the tortoise = (2.1 m/s) * (Total race time - 2 minutes) + 0.2 m

Now, let's solve this equation to find the total race time.

0.14 * Time taken by the tortoise = 2.1 * Total race time - 4.2 + 0.2

0.14 * Time taken by the tortoise = 2.1 * Total race time - 4

0.14 * Time taken by the tortoise - 2.1 * Total race time = -4

Now, we need to note that the race ends when the tortoise reaches the finish line. Therefore, the time taken by the tortoise is equal to the total race time.

So, we can rewrite the equation as:

0.14 * Total race time - 2.1 * Total race time = -4

-1.96 * Total race time = -4

Dividing both sides of the equation by -1.96:

Total race time = -4 / -1.96

Total race time ≈ 2.04 seconds

Therefore, the race takes approximately 2.04 seconds to be completed.