Question

Два комбайна убрали поле за 4 дня.За сколько дней мог бы убрать поле каждый комбайн,если одному из них для выполнения этой работы потребовалось бы на 6 дней меньше,чем другому.ПРОШУ помочь даю много пунктов!

Answer 1

Problem Analysis

We are given that two combines can harvest a field in 4 days. We need to determine how many days it would take for each combine to harvest the field if one of them took 6 days less than the other.

Solution

Let's assume that the first combine takes x days to harvest the field. According to the given information, the second combine takes 6 days less than the first combine, so it would take (x - 6) days to harvest the field.

We know that the combined rate of the two combines is 1 field per 4 days. Therefore, 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 fractions:

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

Simplifying this equation will give us the value of x, which represents the number of days it would take for the first combine to harvest the field.

Let's solve the equation step by step:

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

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 using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For this equation, a = 1, b = -14, and c = 24. Plugging in these values, we get:

x = (-(-14) ± √((-14)^2 - 4(1)(24))) / (2(1))

Simplifying further:

x = (14 ± √(196 - 96)) / 2

x = (14 ± √100) / 2

x = (14 ± 10) / 2

This gives us two possible values for x:

x1 = (14 + 10) / 2 = 12

x2 = (14 - 10) / 2 = 2

Since the number of days cannot be negative, we discard x2 = 2 as a valid solution. Therefore, the first combine would take 12 days to harvest the field.

To find the number of days it would take for the second combine, we subtract 6 from the value of x1:

x2 = x1 - 6 = 12 - 6 = 6

Therefore, the second combine would take 6 days to harvest the field.

Answer

If one of the combines took 6 days less than the other, then the first combine would take 12 days to harvest the field, while the second combine would take 6 days to harvest the field.