Question

Два каменщика укладывают плиткой два одинаковых участка мостовой каждый площадью 140м2 . первый каменщик в день укладывает на 6 м2 плитки больше чем второй, и выполняет всю работу на 3 дня быстрее. Сколько м2 плитки укладывает в день первый каменщик? !!запишите решение и ответ!!!​

Answer 1

Ответ:

20

Объяснение:

Пусть первый каменщик укладывает плиткой в день участок мостовой площадью $x$. Тогда второй каменщик укладывает в день (x − 6) . Получаем уравнение:

$\frac{140}{x-6} -\frac{140}{x} =3$

$140x-140x+840=3x^{2} -18x\\3x^{2} -18x-840=0 |/3\\x^{2} -6x-280=0\\D=6^{2} +4*280=36+1120=1156=34^{2} \\x_{1} =\frac{6+34}{2} =\frac{40}{2} = 20\\x_{2}=\frac{6-36}{2}=-15$

второй х не подходит, т.к он отрицательный

ответ: 20 м^2

Answer 2

Problem Analysis

To solve this problem, we need to determine the rate at which each mason lays the tiles and then use that information to find the rate at which the first mason lays the tiles.

Let's denote: - Rate of the first mason as x m²/day - Rate of the second mason as (x - 6) m²/day (as the first mason lays 6 m² more per day)

We are given that the first mason completes the work 3 days faster than the second mason.

Solution

We can use the formula: time = work/rate to find the time each mason takes to complete the work.

For the first mason: - Time taken = Total work / Rate = 140 m² / x m²/day

For the second mason: - Time taken = Total work / Rate = 140 m² / (x - 6) m²/day

Given that the first mason completes the work 3 days faster than the second mason, we can set up the equation: 140 / x = 140 / (x - 6) - 3

Solving this equation will give us the value of x, which represents the rate at which the first mason lays the tiles.

Calculation

Let's solve the equation: 140 / x = 140 / (x - 6) - 3

Multiplying through by x(x - 6) to clear the fractions: 140(x - 6) = 140x - 3x(x - 6)

Expanding and simplifying: 140x - 840 = 140x - 3x² + 18x 0 = 3x² - 18x - 840

Dividing through by 3: 0 = x² - 6x - 280

Using the quadratic formula to solve for x: x = (-(-6) ± √((-6)² - 4(1)(-280))) / (2(1)) x = (6 ± √(36 + 1120)) / 2 x = (6 ± √1156) / 2 x = (6 ± 34) / 2

We have two potential solutions: 1. x = (6 + 34) / 2 = 40 / 2 = 20 2. x = (6 - 34) / 2 = -28 / 2 = -14

Since the rate cannot be negative, the first mason lays the tiles at a rate of 20 m²/day.

Answer

The first mason lays 20 m² of tiles per day.