Question

Веревку длиной 19,8 м разрезали на две части так, что первая из них оказалась на 20% длинее второй. Найдите длину каждой части

Answer 1

20% = 0,2
Пусть длина первой части х м, тогда длина второй - (х+0,2х) м
х+ (х+0,2х) = 19,8
2,2х=19,8
х=9
1 часть - 9 м
2 часть - 19,8 - 9 = 10,8 м

Answer 2

Problem Analysis

We are given a rope with a length of 19.8 meters that has been cut into two parts. The first part is 20% longer than the second part. We need to find the length of each part.

Solution

Let's assume the length of the second part is x meters. Since the first part is 20% longer than the second part, its length can be expressed as x + 0.2x.

According to the problem, the sum of the lengths of the two parts should be equal to the original length of the rope, which is 19.8 meters. We can write this as an equation:

x + (x + 0.2x) = 19.8

Simplifying the equation:

2.2x = 19.8

Dividing both sides of the equation by 2.2:

x = 19.8 / 2.2

Evaluating the expression:

x = 9

So, the length of the second part is 9 meters.

To find the length of the first part, we can substitute the value of x into the expression x + 0.2x:

9 + 0.2(9) = 9 + 1.8 = 10.8

Therefore, the length of the first part is 10.8 meters.

Answer

The length of the first part is 10.8 meters and the length of the second part is 9 meters.