Question

Голодный волк погнался за зайцем, который был от него на расстоянии 30 м. Скачок волка равен 2 м, а скачок зайца – 1 м. Волк делает 2 скачка за то время, за которое заяц делает 3 скачка. На каком расстоянии волк догонит зайца?

Answer 1

1) 2*2=4(м)-пробежит волк за какое-то время.

2) 3*1=3(м)-пробежит заяц за это-же время.

3) 4-3=1(м)- сократится расстояние между волком и зайцем за 4 метра пробега.

4) 30*4=120(м)- волк догонит зайца.

 

Проверка: соотношение скачков волка и зайца 2/3 ( во время пробежки 120м (волка) волк  сделает 60 скачков, а заяц - 90 скачков по 1 метру. 120-90=на 30  метров меньше, чем волк.

Answer 2

Problem Analysis

We are given that a hungry wolf is chasing a hare that is initially 30 meters away from the wolf. The wolf can jump 2 meters at a time, while the hare can jump 1 meter at a time. The wolf takes 2 jumps for every 3 jumps of the hare. We need to determine at what distance the wolf will catch up to the hare.

Solution

To solve this problem, we can analyze the distances covered by both the wolf and the hare after each set of jumps. Let's break down the problem step by step:

1. Initially, the hare is 30 meters away from the wolf. 2. After the first set of jumps, the wolf covers a distance of 2 * 2 = 4 meters, while the hare covers a distance of 1 * 3 = 3 meters. The distance between the wolf and the hare is now 30 - 4 + 3 = 29 meters. 3. After the second set of jumps, the wolf covers another 4 meters, while the hare covers another 3 meters. The distance between the wolf and the hare is now 29 - 4 + 3 = 28 meters. 4. This pattern continues, with the wolf covering 4 meters and the hare covering 3 meters in each set of jumps. 5. We can see that the distance between the wolf and the hare decreases by 1 meter after each set of jumps. 6. Therefore, the wolf will catch up to the hare when the distance between them becomes 0.

To find the number of sets of jumps required for the wolf to catch up to the hare, we can divide the initial distance of 30 meters by the difference in distances covered by the wolf and the hare in each set of jumps (4 - 3 = 1 meter).

Let's calculate the number of sets of jumps required:

30 / 1 = 30

Therefore, the wolf will catch up to the hare after 30 sets of jumps.

To find the distance at which the wolf catches up to the hare, we can multiply the number of sets of jumps by the distance covered by the wolf in each set of jumps:

30 * 4 = 120

Therefore, the wolf will catch up to the hare at a distance of 120 meters.

Answer

The wolf will catch up to the hare at a distance of 120 meters.

Verification

To verify the answer, let's calculate the distances covered by the wolf and the hare after 30 sets of jumps:

- The wolf covers a distance of 30 sets of jumps * 2 meters per jump = 60 meters. - The hare covers a distance of 30 sets of jumps * 3 meters per jump = 90 meters.

The initial distance between the wolf and the hare was 30 meters. After 30 sets of jumps, the distance between them becomes:

30 - 60 + 90 = 0

Therefore, the answer is verified.