Question

Кошка, мышка и норка находятся на одной прямой. Кошка хочет догнать мышку, а мышка убегает от кошки и хочет спрятаться в норку. Мышке до норки двадцать шагов, Кошке до мышки - восемь прыжков, Кошкин прыжок - девять мышиных шагов, Пока кошка делает один прыжок, мышка делает два шага. Догонит ли кошка мышку?

Answer 1

Нет, кошка не догонит мышку.
Кошке до мышки 8 прыжков. Пока кошка сделает 8 прыжков, мышка пройдет до норки 8*2=16 шагов, то есть между мышкой и кошкой снова расстояние в 16 шагов. Кошка делает еще 1 прыжок и между нею и мышкой 16+2-9=9 шагов, но мышке осталось сделать 2 шага до норки, а кошке до нее один прыжок. Пока кошка делает этот прыжок, мышка уже в норке, а кошка в двух шагах позади нее.

Answer 2

Problem Analysis

In this problem, we are given that a cat, a mouse, and a burrow are located on a straight line. The cat wants to catch the mouse, while the mouse wants to hide in the burrow. We are also given the distances between the mouse and the burrow, the cat and the mouse, and the cat's jump distance in terms of the mouse's steps. We need to determine if the cat will catch the mouse.

Solution

To solve this problem, we need to compare the distances the cat and the mouse need to cover to reach their respective destinations. Let's break down the given information:

- Distance from the mouse to the burrow: 20 steps. - Distance from the cat to the mouse: 8 jumps. - Cat's jump distance: 9 mouse steps. - Mouse's movement: 2 steps for every cat jump.

To determine if the cat will catch the mouse, we need to compare the distances they need to cover. Let's calculate the distances:

- Distance from the cat to the burrow: 8 jumps * 9 mouse steps/jump = 72 mouse steps. - Distance from the mouse to the burrow: 20 steps.

Since the distance from the cat to the burrow (72 mouse steps) is greater than the distance from the mouse to the burrow (20 steps), the cat will not be able to catch the mouse.

Answer: No, the cat will not catch the mouse.

Conclusion

In this problem, we analyzed the distances the cat and the mouse need to cover to reach their respective destinations. By comparing the distances, we determined that the cat will not be able to catch the mouse.