Question

Бригада красит забор длиной 240 метров,ежедневно увеличивая норму покраски на одно и то же число метров.Известно,что за первый и последний день в сумме бригада покрасила 60 метров забора.Определите,сколько дней бригада красила весь забор

Answer 1

1. Бригада маляров красят медленно и даже очень! Считаем таким образом:
Sn – общая площадь
n – количество дней
a1 – первый день
an – последний день
Sn= ((a1+an)/2)*n
n= Sn/((a1+an)/2)
a1+an=60
n= 240/60/2= 8 дней
Ответ: 8 дней

Answer 2

Problem Analysis

We are given that a team is painting a fence that is 240 meters long. The team increases the daily painting norm by the same number of meters each day. It is known that on the first and last day, the team painted a total of 60 meters of the fence. We need to determine how many days it took for the team to paint the entire fence.

Solution

Let's assume that on each day, the team increases the daily painting norm by x meters. On the first day, they painted 60 meters, so the second day they painted 60 + x meters. On the last day, they also painted 60 meters, so the second-to-last day they painted 60 + x meters.

To find the number of days it took for the team to paint the entire fence, we can set up the following equation:

60 + (60 + x) + (60 + 2x) + ... + (60 + (n-1)x) = 240

Simplifying the equation, we get:

60n + x(1 + 2 + ... + (n-1)) = 240

The sum of the first n natural numbers can be calculated using the formula (n(n+1))/2. Substituting this into the equation, we get:

60n + x(n(n-1))/2 = 240

Simplifying further, we have:

60n + xn^2 - xn = 480

Rearranging the equation, we get a quadratic equation:

xn^2 + (60 - x)n - 480 = 0

We can solve this quadratic equation to find the value of n, which represents the number of days it took for the team to paint the entire fence.

Let's solve the quadratic equation using the given information.

Calculation

Using the quadratic formula, we have:

n = (-b ± √(b^2 - 4ac)) / (2a)

where: - a = x - b = 60 - x - c = -480

Substituting the values into the formula, we get:

n = (-(60 - x) ± √((60 - x)^2 - 4x(-480))) / (2x)

Simplifying further, we have:

n = (-(60 - x) ± √(3600 - 120x + x^2 + 1920x)) / (2x)

n = (-(60 - x) ± √(x^2 + 1800x + 3600)) / (2x)

Now, we can solve for n using the given information.

Answer

To determine the number of days it took for the team to paint the entire fence, we need to solve the quadratic equation:

n = (-(60 - x) ± √(x^2 + 1800x + 3600)) / (2x)

Unfortunately, we don't have the value of x (the daily increase in the painting norm) to solve the equation. Without that information, we cannot determine the exact number of days it took for the team to paint the entire fence.

Please provide the value of x (the daily increase in the painting norm) so that we can calculate the number of days.