A speedy tortoise can run at 0.12 m/s, and a

hare can run 18 times as fast. In a race, they
start at the same time, but the hare stops to
rest for 1.5 min, so the tortoise wins by a shell
(20 cm).
How long does the race take?
Answer in units of s

bvsa

To find out how long the race takes, we need to determine the time it takes for both the tortoise and the hare to reach the finish line.

First, let's find the time it takes for the tortoise to run the race. We know the distance the tortoise runs is equal to the distance the hare runs plus the extra distance covered by the tortoise due to the hare resting.

Let's denote the time it takes for the tortoise to complete the race as t (in seconds).

Distance covered by the tortoise = Speed of the tortoise * time taken

Distance covered by the hare = Speed of the hare * time taken

Distance covered by the tortoise = Distance covered by the hare + Extra distance covered by the tortoise

Speed of the hare = 18 * Speed of the tortoise (as given in the question)

Therefore,
Speed of the tortoise * t = (18 * Speed of the tortoise) * t + 0.20 m

Simplifying the equation, we get:
0.12t = 18 * 0.12t + 0.20

0.12t - 18 * 0.12t = 0.20

(1 - 18) * 0.12t = 0.20

-17 * 0.12t = 0.20

-2.04t = 0.20

t = 0.20 / -2.04

t ≈ -0.098 seconds

Since time cannot be negative, this means that the tortoise will never win the race. However, this seems contradictory to the information given in the question. It is possible that there may be an error or inconsistency in the question.

Therefore, we cannot determine the exact time it takes for the race to be completed based on the given information.