Question

Миша и Денис, работая вместе, выполнили задание за 20 ч. Сколько часов необходимо было бы каждому рабочему отдельно на выполнение задания, если Денис может выполнить все задание на 9 ч быстрее Миши? ПЛЗ НАДО ПОМОЩЬ

Answer 1

11 и 9
20-9=11
Первый 11, а другой на 9 больше, те 11+9=20

Answer 2

Task Analysis

To solve this problem, we need to determine the number of hours each worker would need to complete the task separately. We are given that Misha and Denis completed the task together in 20 hours, and Denis can complete the task 9 hours faster than Misha.

Solution

Let's assume that Misha takes x hours to complete the task. Since Denis can complete the task 9 hours faster than Misha, Denis would take (x - 9) hours to complete the task.

When Misha and Denis work together, they complete the task in 20 hours. We can use the formula for the work rate to solve for x:

Work rate = Work / Time

The work rate of Misha is 1/x (1 task completed in x hours), and the work rate of Denis is 1/(x - 9) (1 task completed in x - 9 hours). When they work together, their combined work rate is 1/20 (1 task completed in 20 hours).

Using the formula for the combined work rate:

1/x + 1/(x - 9) = 1/20

To solve this equation, we can multiply through by 20x(x - 9) to eliminate the denominators:

20(x - 9) + 20x = x(x - 9)

Simplifying the equation:

20x - 180 + 20x = x^2 - 9x

40x - 180 = x^2 - 9x

x^2 - 49x + 180 = 0

Now we can solve this quadratic equation to find the value of x, which represents the number of hours Misha would need to complete the task.

Quadratic Equation Solution

Using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = -49, and c = 180.

x = (-(-49) ± √((-49)^2 - 4 * 1 * 180)) / (2 * 1)

Simplifying:

x = (49 ± √(2401 - 720)) / 2

x = (49 ± √1681) / 2

x = (49 ± 41) / 2

We have two possible solutions for x:

1. x = (49 + 41) / 2 = 90 / 2 = 45 2. x = (49 - 41) / 2 = 8 / 2 = 4

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

Therefore, Misha would need 45 hours to complete the task.

Since Denis can complete the task 9 hours faster than Misha, Denis would need 45 - 9 = 36 hours to complete the task.

Answer

If Denis can complete the entire task 9 hours faster than Misha, and Misha would need 45 hours to complete the task, then Denis would need 36 hours to complete the task separately.

Please let me know if you need any further assistance!