Question

Аня и Таня чистят мешок картошки за 56 мин.таня и Аня чистят такой же мешок картошки за 72 мин.Аня и Яна чистят за 63 мин.За сколько минут почистят картошки Аня,Таня и Яна,работая вместе?

Answer 1

72-56= за  16 мин  почистит аня 
56-16= за  40 мин почистит таня 
72-16= за  56 мин почистит  яна 

Answer 2

Problem Analysis

We are given the following information: - Ania and Tanya can clean a bag of potatoes in 56 minutes. - Tanya and Ania can clean the same bag of potatoes in 72 minutes. - Ania and Yana can clean a bag of potatoes in 63 minutes.

We need to determine how long it will take Ania, Tanya, and Yana to clean the bag of potatoes together.

Solution

To solve this problem, we can use the concept of work rates. The work rate is defined as the amount of work done per unit of time. If we let the work rate of Ania, Tanya, and Yana be represented by A, T, and Y respectively, we can set up the following equations:

1. Ania and Tanya can clean a bag of potatoes in 56 minutes: - Their combined work rate is 1/56 of the bag per minute: A + T = 1/56.

2. Tanya and Ania can clean the same bag of potatoes in 72 minutes: - Their combined work rate is 1/72 of the bag per minute: T + A = 1/72.

3. Ania and Yana can clean a bag of potatoes in 63 minutes: - Their combined work rate is 1/63 of the bag per minute: A + Y = 1/63.

We can solve this system of equations to find the individual work rates of Ania, Tanya, and Yana. Then, we can calculate the time it will take for them to clean the bag of potatoes together.

Let's solve the system of equations step by step:

1. Subtract equation 2 from equation 1 to eliminate T: - (A + T) - (T + A) = (1/56) - (1/72) - A - T = 1/56 - 1/72 - A - T = 4/252 - 3/252 - A - T = 1/252

2. Subtract equation 3 from equation 1 to eliminate Y: - (A + Y) - (A + T) = (1/56) - (1/63) - A - T = 1/56 - 1/63 - A - T = 9/504 - 8/504 - A - T = 1/504

Now we have two equations with two variables (A - T = 1/252 and A - T = 1/504). Since the left sides of both equations are the same, the right sides must also be the same. Therefore, we can conclude that 1/252 = 1/504.

Let's calculate the time it will take for Ania, Tanya, and Yana to clean the bag of potatoes together:

- Ania's work rate (A) = 1/252 of the bag per minute. - Tanya's work rate (T) = 1/252 of the bag per minute. - Yana's work rate (Y) = 1/63 of the bag per minute.

The combined work rate of Ania, Tanya, and Yana is A + T + Y.

To find the time it will take for them to clean the bag of potatoes together, we can use the formula:

Time = 1 / (A + T + Y)

Let's calculate the time:

Time = 1 / (1/252 + 1/252 + 1/63) = 1 / (3/252 + 4/252 + 4/252) = 1 / (11/252) = 252 / 11 ≈ 22.909 minutes

Therefore, it will take Ania, Tanya, and Yana approximately 22.909 minutes to clean the bag of potatoes together.

Answer

Ania, Tanya, and Yana will clean the bag of potatoes together in approximately 22.909 minutes.