Question

Два майстри, працюючи рівномірно, але з різною продуктивністю, виконали завдання за 20 год. Якби перший майстер виконав 1/3 завдання, а потім другий решту, то загальний затрачений час дорівнював би 50 год. За скільки часу може виконати завдання перший майстер, працюючи окремо? (Вважати, що час менший 100 год.)

Answer 1

Розв'язання завдання додаю

Answer 2

Problem Analysis

We are given that two workers completed a task in 20 hours while working at different levels of productivity. If the first worker completed 1/3 of the task and the second worker completed the rest, the total time would have been 50 hours. We need to determine how long it would take for the first worker to complete the task alone.

Solution

Let's assume that the first worker's productivity is represented by x (in terms of the fraction of the task completed per hour) and the second worker's productivity is represented by y.

According to the given information, if the first worker completed 1/3 of the task, it means that the second worker completed 2/3 of the task. Therefore, we can write the following equation:

x * 20 + y * 20 = 1/3 + 2/3 = 1 This equation represents the total amount of work done by both workers in 20 hours.

If the first worker were to complete the entire task alone, we can set up the following equation:

x * t = 1, where t represents the time taken by the first worker alone.

Now, we can solve this equation to find the value of t.

Calculation

Let's solve the equation x * t = 1 for t using the information from equation.

From equation we have x * 20 + y * 20 = 1.

Since the first worker completed 1/3 of the task, we can write x = 1/3.

Substituting this value into the equation, we get:

(1/3) * 20 + y * 20 = 1

Simplifying the equation:

(20/3) + 20y = 1

Multiplying both sides by 3 to eliminate the fraction:

20 + 60y = 3

Simplifying further:

60y = 3 - 20

60y = -17

Dividing both sides by 60:

y = -17/60

Now, we can substitute the value of y back into the equation x * t = 1 to find the value of t:

(1/3) * t = 1

Multiplying both sides by 3:

t = 3

Therefore, the first worker can complete the task alone in 3 hours.

Answer

The first worker can complete the task alone in 3 hours.