Question

Для виконання малярних робіт одному робітникові потрібно на 5 днів менше, ніж другому. Роботу вони розпочали разом та за 4 дні виконали 2/3 усієї роботи. Визначити, за який час кожний з них окремо може вико­нати такий обсяг роботи.

Answer 1

Пояснення:

Приймаємо весь обсяг роботи за одиницю (1).

Нехай час, за який перший робітник окремо може вико­нати такий обсяг робіт дорівнює х, а час, за який другий робітник окремо може вико­нати такий обсяг робіт дорівнює у.            ⇒

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Відповідь: перший робітник окремо може вико­нати такий обсяг робіт за 15 годин, другий робітник окремо може вико­нати такий обсяг робіт за 10 годин.

Answer 2

Problem Analysis

We are given that one worker can complete a painting job in 5 days less than another worker. They started the job together and after 4 days, they have completed 2/3 of the entire job. We need to determine how long each worker individually can complete the same amount of work.

Solution

Let's assume that the first worker can complete the job in x days. This means that the second worker can complete the job in (x + 5) days, as they take 5 days longer.

We are given that they started the job together and after 4 days, they have completed 2/3 of the entire job. This means that in 4 days, they have completed 2/3 of the work.

To find the individual rates of each worker, we can set up the following equation:

Worker 1's rate * 4 days + Worker 2's rate * 4 days = 2/3 of the work

Let's solve this equation to find the individual rates of each worker.

Calculation

Let's assume that Worker 1 can complete the job in x days. This means that Worker 2 can complete the job in (x + 5) days.

According to the given information, in 4 days, they have completed 2/3 of the work. This means that:

Worker 1's rate * 4 days + Worker 2's rate * 4 days = 2/3 of the work

Let's solve this equation:

4/x + 4/(x + 5) = 2/3

To simplify the equation, we can multiply through by 3x(x + 5):

12(x + 5) + 12x = 2x(x + 5)

Expanding and simplifying:

12x + 60 + 12x = 2x^2 + 10x

Rearranging and simplifying:

2x^2 - 14x - 60 = 0

Dividing through by 2:

x^2 - 7x - 30 = 0

Factoring the quadratic equation:

(x - 10)(x + 3) = 0

This gives us two possible values for x: x = 10 or x = -3.

Since the number of days cannot be negative, we can discard the solution x = -3.

Therefore, Worker 1 can complete the job in 10 days, and Worker 2 can complete the job in (10 + 5) = 15 days.

Answer

Based on the given information, Worker 1 can complete the same amount of work in 10 days, while Worker 2 can complete the same amount of work in 15 days.