Question

Плз помогите решить задачу. два каменщика сложили вместе стенку в 20 дней. За сколько дней выполнил бы работу каждый из них отдельно, если известно, что первый каменщик должен работать на 9 дней больше второго?

Answer 1

Решение:

х+х+9=20

2х+9=20

2х=20-9

2х=11

х=5,5

5,5+9=14,5

Answer 2

Problem Analysis

We are given that two bricklayers together completed a wall in 20 days. We need to determine how many days each bricklayer would take to complete the work individually if the first bricklayer works 9 days more than the second bricklayer.

Solution

Let's assume that the second bricklayer takes x days to complete the work. Since the first bricklayer works 9 days more than the second bricklayer, the first bricklayer would take x + 9 days to complete the work.

To find the individual work rates, we can use the formula:

Work Rate = Work / Time

The work rate of the first bricklayer is the work completed by the first bricklayer in one day, and the work rate of the second bricklayer is the work completed by the second bricklayer in one day.

Since both bricklayers together completed the work in 20 days, their combined work rate is:

Combined Work Rate = 1 / 20

To find the individual work rates, we can set up the following equation:

First Bricklayer's Work Rate + Second Bricklayer's Work Rate = Combined Work Rate

Let's solve the equation to find the individual work rates.

Calculation

Let's assume the second bricklayer takes x days to complete the work. Therefore, the first bricklayer takes x + 9 days to complete the work.

The combined work rate is given by:

Combined Work Rate = 1 / 20

The equation for the individual work rates is:

(1 / (x + 9)) + (1 / x) = 1 / 20

To solve this equation, we can multiply through by the common denominator (20 * x * (x + 9)):

20 * x + 20 * (x + 9) = x * (x + 9)

Simplifying the equation:

20x + 20x + 180 = x^2 + 9x

40x + 180 = x^2 + 9x

Rearranging the equation:

x^2 + 9x - 40x - 180 = 0

x^2 - 31x - 180 = 0

Now we can solve this quadratic equation to find the value of x.

Quadratic Equation Solution

Using the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

For our equation x^2 - 31x - 180 = 0, a = 1, b = -31, and c = -180.

Substituting the values into the quadratic formula:

x = (-(-31) ± sqrt((-31)^2 - 4 * 1 * (-180))) / (2 * 1)

Simplifying:

x = (31 ± sqrt(961 + 720)) / 2

x = (31 ± sqrt(1681)) / 2

x = (31 ± 41) / 2

We have two possible solutions:

1. x = (31 + 41) / 2 = 72 / 2 = 36 2. x = (31 - 41) / 2 = -10 / 2 = -5

Since the number of days cannot be negative, we discard the second solution.

Therefore, the second bricklayer would take 36 days to complete the work.

The first bricklayer would take 36 + 9 = 45 days to complete the work.

Answer

If the first bricklayer works 9 days more than the second bricklayer, then the second bricklayer would take 36 days to complete the work, and the first bricklayer would take 45 days to complete the work.

Note: The answer is based on the assumption that the work rates of the bricklayers are constant throughout the project.