Question

В бассейн ведет несколько труб, они заливают воду в бассейн с одинаковой скоростью. Бассейн каждый день наполняется заново. В понедельник несколько труб наполнили бассейн. Во вторник подключили на одну трубу больше, чем в понедельник, в результате чего бассейн наполнился на 8 минут быстрее. В среду подключили на 4 трубы больше, чем во вторник, и бассейн наполнился на 16 минут быстрее, чем во вторник. Сколько труб работало в понедельник?

Answer 1

Ответ: в понедельник работало 5 труб.

Answer 2

Number of Pipes Working Each Day

To solve this problem, we can use a system of equations to represent the situation and solve for the number of pipes working on Monday.

Let's denote: - x as the number of pipes working on Monday - y as the time it takes to fill the pool on Monday

We are given the following information: 1. On Monday, the pool was filled by x pipes. 2. On Tuesday, one more pipe was added, and the pool was filled 8 minutes faster than on Monday. 3. On Wednesday, four more pipes were added, and the pool was filled 16 minutes faster than on Tuesday.

We can use this information to form a system of equations and solve for x.

System of Equations

1. For Monday: - Number of pipes: x - Time taken: y

2. For Tuesday: - Number of pipes: x + 1 - Time taken: y - 8

3. For Wednesday: - Number of pipes: x + 5 - Time taken: y - 24

Solving the System of Equations

We can use the information from Tuesday and Wednesday to form two equations and solve for x.

From the information given: - (x + 1) pipes took (y - 8) minutes on Tuesday - (x + 5) pipes took (y - 24) minutes on Wednesday

We can set up the following equations: 1. (x + 1) pipes took (y - 8) minutes: (x + 1)y = (x(y - 8)) 2. (x + 5) pipes took (y - 24) minutes: (x + 5)y = (x(y - 24))

By solving these equations, we can find the value of x.

Let's calculate the value of x using the given information.