Question

Мотузку розрізали на 5 рівних частин. Іншу мотузку, довжина якої на 10 м більша, розрізали на сім таких самих частин. Знайти початкову довжину кожної мотузки.

Answer 1

Другу мотузку розрізали на 2 частини більше і довжина її на 10 м більша.
Отже, одна частина мотузки рівна 10/2=5 м.
5*5=25 м - довжина першої мотузки.
5*7=35 м - довжина другої мотузки.

Answer 2

Finding the Initial Length of Each Rope

To find the initial length of each rope, we can use a system of equations based on the given information.

Let's assume the initial length of the first rope is x meters.

According to the problem, the first rope was cut into 5 equal parts. Therefore, the length of each part is x/5 meters.

The second rope, which is 10 meters longer than the first rope, has an initial length of x + 10 meters.

This second rope was cut into 7 equal parts. Therefore, the length of each part is (x + 10)/7 meters.

To find the initial length of each rope, we need to solve the following system of equations:

Equation 1: x/5 = (x + 10)/7

To solve this equation, we can cross-multiply:

7x = 5(x + 10)

7x = 5x + 50

2x = 50

x = 25

Therefore, the initial length of the first rope is 25 meters.

To find the initial length of the second rope, we can substitute the value of x into the equation:

x + 10 = 25 + 10 = 35

Therefore, the initial length of the second rope is 35 meters.

In summary, the initial length of each rope is:

- The first rope: 25 meters - The second rope: 35 meters.

Please let me know if you need any further assistance!