Question

Два зайчика Сластена и Соня одновременно начинают прыгать с линии старта в одном и том же направлении. Каждый из них делает один скачок в секунду. Соня первый раз прыгнула на 1 м, а каждый следующий его прыжок был на 1 м длиннее предыдущего. Сластена каждый раз прыгал на 3 м. Через сколько прыжков Соня догнал Сластену?

Answer 1

1+2+3+4+5=15
3*5=15
Ответ: через 5 прыжков.

Answer 2

Problem Analysis

We have two rabbits, Slastena and Sonya, who start jumping from the same starting line in the same direction. Sonya jumps 1 meter on her first jump, and each subsequent jump is 1 meter longer than the previous one. Slastena, on the other hand, jumps 3 meters each time. We need to determine how many jumps it will take for Sonya to catch up to Slastena.

Solution

To solve this problem, we can set up an equation to represent the distance covered by each rabbit after a certain number of jumps. Let's assume that after n jumps, Sonya has covered a total distance of D_s meters, and Slastena has covered a total distance of D_sl meters.

For Sonya: - Distance covered after the first jump: 1 meter - Distance covered after the second jump: 1 + 2 = 3 meters - Distance covered after the third jump: 1 + 2 + 3 = 6 meters - Distance covered after the fourth jump: 1 + 2 + 3 + 4 = 10 meters

We can observe that the distance covered by Sonya after n jumps can be represented by the sum of the first n natural numbers: D_s = 1 + 2 + 3 + ... + n.

For Slastena: - Distance covered after the first jump