Question

Два робітники, працюючи разом, можуть виконати завдання за 4год. За скільки годин може виконати завдання кожен робітник, працюючи самостійно, якщо один з них може це зробить на 6год. швидше, ніж інший?

Answer 1

4*2=8.8-6=2  один за 8 а другой за 2

Answer 2

Task Analysis

We are given that two workers can complete a task together in 4 hours. We need to determine how many hours each worker would take to complete the task individually if one of them can do it 6 hours faster than the other.

Solution

Let's assume that the first worker takes x hours to complete the task on their own. Since the second worker can do the task 6 hours faster, they would take (x - 6) hours to complete the task individually.

To find the combined work rate of the two workers, we can use the concept of "work done = rate × time". The combined work rate is the sum of the individual work rates.

The work done by the first worker in 1 hour is 1/x of the task, and the work done by the second worker in 1 hour is 1/(x - 6) of the task.

According to the given information, when the two workers work together, they can complete the task in 4 hours. Therefore, their combined work rate is 1/4 of the task per hour.

Using this information, we can set up the following equation:

1/x + 1/(x - 6) = 1/4

To solve this equation, we can multiply through by 4x(x - 6) to eliminate the denominators:

4(x - 6) + 4x = x(x - 6)

Simplifying the equation:

4x - 24 + 4x = x^2 - 6x

8x - 24 = x^2 - 6x

Rearranging the equation:

x^2 - 14x + 24 = 0

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

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a), where a = 1, b = -14, and c = 24.

Calculating the discriminant: b^2 - 4ac = (-14)^2 - 4(1)(24) = 196 - 96 = 100

Since the discriminant is positive, there are two real solutions for x.

Using the quadratic formula:

x = (-(-14) ± √(100)) / (2(1)) x = (14 ± 10) / 2

Simplifying:

x1 = (14 + 10) / 2 = 24 / 2 = 12 x2 = (14 - 10) / 2 = 4 / 2 = 2

Therefore, the two workers can complete the task individually in 12 hours and 2 hours, respectively.

Answer

If one of the workers can complete the task in 6 hours faster than the other, then the worker who can complete the task in 12 hours would take 12 hours to complete the task individually, and the worker who can complete the task in 2 hours would take 2 hours to complete the task individually.