Question

Два мастера оклеили обоями квартиры на этаже в новом доме за 15 дней причем второй присоединился к первому через 7 дней после начала работы. Известно что первому мастеру на выполнение работы потребовалось бы на7 дней меньше чем второму. За сколько дней мог бы выполнить эту работу каждый мастер работая отдельно!?? Со всеми пояснинеиями плиззз

Answer 1

Х дней потратил бы на всю работу первый мастер.
Х+7 дней потратил бы второй мастер.

1/х производительность первого.

1/х+7 производителоьность второго.

по условию видими что первый мастер работал 15 дней, а второй на 7 меньше, т.е. 8 дней.
составляем уравнение:

(15/х) + ( 8/(х+7) ) =1

и умножаем все уравнение на х(х+7)
получается: 15х+105+8х=х^2+7х
х^2-16х-105=0
Дискриминант. =26. И х1=-5, х2=21.
дни отрицательными бытть не могут, поэтому берем число 21.
21+7=28.
Ответ: 21 дней-первый мастер. 28 дней- второй мастер.

Answer 2

Problem Analysis

We have two masters who wallpapered the apartments on a floor in a new building. The second master joined the first one after 7 days. We know that the first master would have taken 7 days less than the second master to complete the work. We need to determine how many days each master would take to complete the work individually.

Solution

Let's assume that the first master takes x days to complete the work. Therefore, the second master would take x + 7 days to complete the work.

To find the total time taken by both masters working together, we can use the formula:

1 / (x) + 1 / (x + 7) = 1 / 15

Simplifying the equation:

(x + 7 + x) / (x * (x + 7)) = 1 / 15

Multiplying both sides by 15 * x * (x + 7):

15 * (2x + 7) = x * (x + 7)

Expanding and simplifying:

30x + 105 = x^2 + 7x

Rearranging the equation:

x^2 - 23x - 105 = 0

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

Using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = -23, and c = -105.

Calculating the discriminant:

D = b^2 - 4ac = (-23)^2 - 4(1)(-105) = 529 + 420 = 949

Since the discriminant is positive, we have two real solutions for x.

Using the quadratic formula:

x = (-(-23) ± √(949)) / (2 * 1)

Simplifying:

x = (23 ± √949) / 2

Calculating the two possible values of x:

x1 = (23 + √949) / 2 ≈ 20.97 x2 = (23 - √949) / 2 ≈ 2.03

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

Therefore, the first master would take approximately 20.97 days to complete the work if working alone.

To find the number of days the second master would take, we add 7 to the value of x:

x + 7 ≈ 20.97 + 7 ≈ 27.97

Therefore, the second master would take approximately 27.97 days to complete the work if working alone.

Answer

If each master worked individually, the first master would take approximately 20.97 days to complete the work, and the second master would take approximately 27.97 days to complete the work.