Question

Собака заметила зайца на расстоянии 120 м.Если заяц победит со скоростью 10 м/с, то собака догонит за 36 сек.С какой минимальной скоростью надо бежать зайцу, чтоб его не догнала собака?

Answer 1

Заяц бежит со скоростью 10 м/с. Получается, за 36 секунд он пробежит 360 метров. За та же 36 секунд собака пробежит 360 + 120 = 480 метров. Получается, что скорость собаки равна 480 метров / 36 секунд = 13 метров в секунду. 

Значит, зайцу надо бежать быстрее 13 метров в секунду)

Answer 2

Problem Analysis

We are given that a dog notices a hare at a distance of 120 meters. If the hare runs at a speed of 10 m/s, the dog will catch up to it in 36 seconds. We need to determine the minimum speed at which the hare should run in order to avoid being caught by the dog.

Solution

Let's assume that the minimum speed at which the hare should run to avoid being caught by the dog is v m/s.

We can use the formula distance = speed × time to calculate the distance covered by both the dog and the hare.

For the dog: - Distance covered by the dog = 120 meters - Time taken by the dog = 36 seconds

For the hare: - Distance covered by the hare = 120 + (v × 36) meters - Time taken by the hare = 36 seconds

Since the distance covered by the dog and the hare is the same, we can equate the two distances and solve for v.

Calculation

120 = 10 × 36 + v × 36

Simplifying the equation: 120 = 360 + 36v

Rearranging the equation: 36v = 120 - 360 36v = -240

Dividing both sides by 36: v = -240/36 v = -6.67

Since speed cannot be negative, we can conclude that the hare needs to run at a minimum speed of 6.67 m/s in order to avoid being caught by the dog.

Answer

The hare needs to run at a minimum speed of 6.67 m/s in order to avoid being caught by the dog.

Explanation

If the hare runs at a speed of 6.67 m/s, it will cover a distance of 240 meters in 36 seconds. This will allow the hare to stay ahead of the dog, which covers a distance of 120 meters in the same time period. Therefore, the hare will not be caught by the dog.

Note: The negative value obtained during the calculation is due to the assumption made in the problem statement. The negative value indicates that the hare needs to run in the opposite direction to avoid being caught by the dog. However, in reality, the hare cannot run in the opposite direction, so the minimum speed required to avoid being caught is 6.67 m/s.