Question

Пятачок и Винни-Пух вышли из дома Пятачка и направились к дому Винни-Пуха. Длина  шага Пятачка на 10% короче, чем у Винни-Пуха. За одинаковый промежуток времени число шага Пятасчка на 20% больше, чем число шагов Винни-Пух. Кто из них быстрее дойдет до дома Виннни-Пуха?

Answer 1

Problem Analysis

We are given that Piglet and Winnie-the-Pooh leave Piglet's house and head towards Winnie-the-Pooh's house. We are also given the following information: - Piglet's step length is 10% shorter than Winnie-the-Pooh's step length. - Piglet takes 20% more steps than Winnie-the-Pooh in the same amount of time.

We need to determine who will reach Winnie-the-Pooh's house faster.

Solution

Let's assume that Winnie-the-Pooh takes x steps to reach his house. Since Piglet takes 20% more steps than Winnie-the-Pooh, Piglet will take 1.2x steps to cover the same distance.

We are also given that Piglet's step length is 10% shorter than Winnie-the-Pooh's step length. Let's assume Winnie-the-Pooh's step length is y. Therefore, Piglet's step length will be 0.9y.

To find the distance covered by each character, we can multiply the number of steps by the step length. The distance covered by Winnie-the-Pooh will be xy, and the distance covered by Piglet will be 1.2xy.

Since both characters start at the same time and cover the same distance, we can compare their speeds by dividing the distance covered by the time taken. Let's assume the time taken is t.

The speed of Winnie-the-Pooh will be xy / t, and the speed of Piglet will be 1.2xy / t.

To determine who will reach Winnie-the-Pooh's house faster, we need to compare their speeds. If Piglet's speed is greater, Piglet will reach the house faster. If Winnie-the-Pooh's speed is greater, Winnie-the-Pooh will reach the house faster.

Let's calculate the speeds and compare them.

Calculation

Let's assume the step length of Winnie-the-Pooh is 1 unit (y = 1). Therefore, Piglet's step length will be 0.9 units.

The number of steps taken by Winnie-the-Pooh will be x. The number of steps taken by Piglet will be 1.2x.

The distance covered by Winnie-the-Pooh will be xy = 1x = x. The distance covered by Piglet will be 1.2xy = 1.2x.

The speed of Winnie-the-Pooh will be xy / t = x / t. The speed of Piglet will be 1.2xy / t = 1.2x / t.

To compare their speeds, we can divide the speed of Piglet by the speed of Winnie-the-Pooh: (1.2x / t) / (x / t) = (1.2x / t) * (t / x) = 1.2.

Conclusion

From the calculations, we can see that the speed of Piglet is 1.2 times the speed of Winnie-the-Pooh. Therefore, Piglet will reach Winnie-the-Pooh's house faster.

Please note that the above calculations are based on the assumptions made regarding step lengths and time taken. The actual values may vary depending on the specific details of the problem.