Question

Два токаря, работая совместно, могут выполнить задание за 15 дней. Вначале они работали совместно 5 дней. Остальную часть задания первый токарь закончил за 16 дней. За сколько дней может выполнить задание 1-ый токарь? Второй токарь?

Answer 1

Решение в приложении

Answer 2

Task Analysis

We have two lathe operators working together to complete a task in 15 days. They initially work together for 5 days, and then the first operator completes the remaining part of the task in 16 days. We need to determine how many days it would take for the first operator to complete the entire task and how many days it would take for the second operator to complete the entire task.

Solution

Let's assume that the first operator can complete the entire task in x days and the second operator can complete the entire task in y days.

From the given information, we know that: - The two operators working together can complete the task in 15 days. - They initially work together for 5 days, which means they complete 5/15th of the task. - The first operator completes the remaining part of the task in 16 days.

Based on this information, we can set up the following equations:

Equation 1: (5/15) + (5/x) = 1 (The fraction of the task completed by the first operator in 5 days plus the fraction completed by the first operator in x days should equal 1, representing the entire task.)

Equation 2: (10/15) + (10/y) = 1 (The fraction of the task completed by both operators in 10 days plus the fraction completed by the second operator in y days should equal 1, representing the entire task.)

Now, let's solve these equations to find the values of x and y.

Solving the Equations

To solve Equation 1, we can simplify it by multiplying both sides by 15x: (5x) + (75) = 15x

Simplifying further: 75 = 15x - 5x 75 = 10x x = 7.5

Therefore, the first operator can complete the entire task in 7.5 days.

To solve Equation 2, we can simplify it by multiplying both sides by 15y: (10y) + (150) = 15y

Simplifying further: 150 = 15y - 10y 150 = 5y y = 30

Therefore, the second operator can complete the entire task in 30 days.

Answer

Based on the given information, the first operator can complete the entire task in 7.5 days and the second operator can complete the entire task in 30 days.

Note: The calculations are based on the given information and assumptions made.