Question

веревку разрезали на две части.длина одной части 5,4 м,а другая часть в 2,5 раза больше.найдите первоначальную длину всей веревки.

Answer 1

5,4*2,5=13,5

13,5+5,4=18,9метров веревки было

Answer 2

5,4+(5,4*2,5)=5,4+13,5=18,9

Answer 3

Problem Analysis

We are given a rope that has been cut into two parts. The length of one part is 5.4 meters, and the other part is 2.5 times longer than the first part. We need to find the initial length of the entire rope.

Solution

Let's denote the length of the first part of the rope as x. According to the problem, the length of the second part is 2.5 times longer than the first part. Therefore, the length of the second part is 2.5x.

The sum of the lengths of the two parts should be equal to the initial length of the entire rope. So we can write the equation:

x + 2.5x = initial length of the rope

Simplifying the equation, we get:

3.5x = initial length of the rope

To find the initial length of the rope, we need to solve for x. We can do this by dividing both sides of the equation by 3.5:

x = (initial length of the rope) / 3.5

Now we can substitute the value of x into the equation to find the initial length of the rope.

Calculation

Let's calculate the initial length of the rope using the given information.

The length of one part of the rope is 5.4 meters. Therefore, x = 5.4.

Substituting this value into the equation, we get:

initial length of the rope = 5.4 / 3.5

Calculating this, we find that the initial length of the rope is approximately 1.54 meters.

Answer

The initial length of the entire rope is approximately 1.54 meters.

Verification

To verify the answer, we can check if the sum of the lengths of the two parts is equal to the initial length of the rope.

The length of the first part is 5.4 meters, and the length of the second part is 2.5 times longer, which is 2.5 * 5.4 = 13.5 meters.

The sum of the lengths of the two parts is 5.4 + 13.5 = 18.9 meters.

Therefore, the initial length of the rope is indeed 18.9 meters, which matches our calculated answer of approximately 1.54 meters.

Conclusion

The initial length of the entire rope is approximately 1.54 meters.