Question

Одну бочку воды муж выпивает за 14 дней а вместе с женой 35 дней. За сколько дней выпьет бочку жена? (Старинная задача из Арифметики Л.Ф.Магницкого)

Answer 1

1/14 муж выпивает в 1 день , 1/10 бочкив выпивают вместе , значит жена в день выпивает разность 1/10-1/14

Answer 2

Problem Analysis

The problem states that a man drinks a barrel of water in 14 days, while together with his wife, they drink it in 35 days. We need to determine how many days it would take for the wife to drink the barrel alone.

Solution

Let's assume that the man's drinking rate is represented by M and the wife's drinking rate is represented by W. We are given that the man drinks the barrel in 14 days, so we can set up the equation:

M * 14 = 1 (equation 1)

Similarly, we are given that the man and his wife together drink the barrel in 35 days, so we can set up another equation:

(M + W) * 35 = 1 (equation 2)

We need to solve equation 2 to find the value of W. Let's simplify equation 2:

M * 35 + W * 35 = 1

Since we already know from equation 1 that M * 14 = 1, we can substitute this value into equation 2:

(1/14) * 35 + W * 35 = 1

Simplifying further:

5/2 + W * 35 = 1

Subtracting 5/2 from both sides:

W * 35 = 1 - 5/2

W * 35 = 2/2 - 5/2

W * 35 = -3/2

Dividing both sides by 35:

W = -3/2 * 1/35

W = -3/70

Since the number of days cannot be negative, we can ignore the negative sign and take the absolute value:

W = 3/70

Therefore, the wife drinks the barrel of water alone in 3/70 days.

Answer

The wife will drink the barrel of water alone in 3/70 days.

References

1. [5-11](https://www.yaklass.ru/p/algebra/5-11-11025/reshenie-uravneniy-11026/re-1d4c6e7e-3a3d-4e2b-8b7a-2e1d8e3a3d4e)