Question

Два работника, работая вместе, могут выполнить, некоторую работу в 12 дней, но на самом деле вместе они работали только 3 дня, после чего первый прекратил работу, а второму понадобилось еще 21 день, чтобы закончить эту работу. Во сколько дней каждый работник, работая отдельно, может выполнить эту работу? В ответ дайте сумму этих величин.​

Answer 1

Работая вместе 3 дня сделали четверть работы ( от всей 12 дневной)

Осталось три четверти .

Второй три четверти работы выполнил за 21 день - значит всю ( четыре четверти ) за 28 дней.

Работая 84 дня вместе выполнили бы 84/12 = 7 работ.

Второй за 84 дня выполнил бы 84/28 = 3 работы. Значит первый за 84 дня выполнил бы 7-3= 4 работы . Или за 84/4 = 21 день одну работу.

В ответе требуют сумму 21+28 = 49

Answer 2

Problem Analysis

We are given that two workers can complete a certain task together in 12 days. However, in reality, they only worked together for 3 days. After that, the first worker stopped working, and it took the second worker an additional 21 days to complete the task. We need to determine how many days each worker would take to complete the task individually and provide the sum of those values.

Solution

Let's assume that the first worker can complete the task in x days and the second worker can complete the task in y days. We can use the concept of "work done" to solve this problem.

The work done by the first worker in 3 days is equal to the work done by both workers in 12 days. Similarly, the work done by the second worker in 21 days is also equal to the work done by both workers in 12 days.

Using this information, we can set up the following equations:

Equation 1: 3/x + 3/y = 1/12 (work done by the first worker in 3 days is equal to 1/12 of the total work) Equation 2: 21/y = 1/12 (work done by the second worker in 21 days is equal to 1/12 of the total work)

To solve these equations, we can rearrange Equation 1 to solve for y and substitute the value of y in Equation 2.

Calculation

Let's solve the equations to find the values of x and y.

From Equation 1: 3/x + 3/y = 1/12

Multiplying both sides by 12xy: 36y + 36x = xy

Rearranging the equation: xy - 36x - 36y = 0

Using the quadratic formula: y = (36 ± sqrt(36^2 - 4x(-36)))/(2x) y = (36 ± sqrt(1296 + 144x))/(2x)

Substituting the value of y in Equation 2: 21/y = 1/12

Cross-multiplying: 21*12 = y y = 252

Substituting the value of y in the equation for x: 252 = (36 ± sqrt(1296 + 144x))/(2x)

Simplifying the equation: 504x = 36 ± sqrt(1296 + 144x)

Squaring both sides: (504x)^2 = (36 ± sqrt(1296 + 144x))^2

Expanding and simplifying: 254016x^2 - 72x ± 1296 = 0

Using the quadratic formula: x = (-(-72) ± sqrt((-72)^2 - 4*254016*1296))/(2*254016) x = (72 ± sqrt(5184 - 1327104))/(508032) x = (72 ± sqrt(-1321920))/(508032)

Since the square root of a negative number is not possible in this context, there are no real solutions for x. Therefore, we cannot determine the number of days it would take for each worker to complete the task individually.

Answer

Based on the given information, we cannot determine the number of days it would take for each worker to complete the task individually.