Question

Одна робота три мальчика (A,B,C) Если А и В вместе сделают эту работу то успеют за 12 дней т.е А+В=12 В+С=15 А+С=20 дней Найдите за сколько дней уложится А в одиночку : 30

Answer 1

Система: 
(1/a) + (1/b) = 1/12 
(1/b) + (1/c) = 1/15 
(1/a) + (1/c) = 1/20
------------------------- можно сложить все три уравнения
2*((1/a) + (1/b) + (1/с)) = (1/12) + (1/15) + (1/20) =
 = (5+4+3) / (3*4*5) 
(1/a) + (1/b) + (1/с) = 1/10 (т.е. втроем они выполнят всю работу за 10 дней)
из первого уравнения: 1/c = (1/10) - (1/12) = (6-5) / (2*5*6) = 1/60 
(т.е. С в одиночестве выполнит работу за 60 дней)
из третьего уравнения: 1/а = (1/20) - (1/60) = (3-1) / 60 = 1/30 
(т.е. А в одиночестве выполнит работу за 30 дней)

Answer 2

Problem Analysis

We are given that three boys, A, B, and C, are working together on a task. If A and B work together, they can complete the task in 12 days. If B and C work together, they can complete the task in 15 days. And if A and C work together, they can complete the task in 20 days. We need to find out how many days it will take for A to complete the task alone.

Solution

Let's assume that A can complete the task alone in x days.

From the given information, we can derive the following equations:

1. If A and B work together, they can complete the task in 12 days: A + B = 12. 2. If B and C work together, they can complete the task in 15 days: B + C = 15. 3. If A and C work together, they can complete the task in 20 days: A + C = 20.

We need to solve these equations to find the value of x.

To solve these equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From equation 1, we can express B in terms of A: B = 12 - A.

Substituting this value of B in equation 2, we get: (12 - A) + C = 15.

Simplifying the equation, we get: C = 15 - 12 + A.

Substituting the values of A and C in equation 3, we get: A + (15 - 12 + A) = 20.

Simplifying the equation, we get: 2A = 17.

Solving for A, we find: A = 8.5.

Therefore, A can complete the task alone in 8.5 days.

Answer

A can complete the task alone in 8.5 days.