Question

Двое рабочих изготовили 400 деталей за 8 часов. определить производительность первого рабочего если в одиночку он может выполнить всю работу за 6 часов 40 минут быстрее второго

Answer 1

Problem Analysis

We are given that two workers together produced 400 parts in 8 hours. We need to determine the productivity of the first worker if they can complete the entire job 6 hours and 40 minutes faster than the second worker.

Solution

Let's assume the productivity of the first worker is x parts per hour. The productivity of the second worker can be calculated using the formula:

Productivity of the second worker = Total productivity - Productivity of the first worker

The total productivity is given by:

Total productivity = 400 parts / 8 hours = 50 parts per hour

Substituting the values, we get:

Productivity of the second worker = 50 parts per hour - x parts per hour

We also know that the first worker can complete the entire job in 6 hours and 40 minutes faster than the second worker. This means that the second worker takes 6 hours and 40 minutes longer to complete the job than the first worker.

Converting 6 hours and 40 minutes to hours, we get:

6 hours + (40 minutes / 60 minutes per hour) = 6.67 hours

So, the time taken by the second worker is:

Time taken by the second worker = Time taken by the first worker + 6.67 hours

Now, we can calculate the productivity of the first worker using the formula:

Productivity = Total parts / Total time

Let's substitute the values and calculate the productivity of the first worker.

Calculation

Total productivity = 400 parts / 8 hours = 50 parts per hour

Time taken by the second worker = Time taken by the first worker + 6.67 hours

Productivity of the second worker = Total productivity - Productivity of the first worker

Productivity of the first worker = Total parts / Total time

Solution

The productivity of the first worker is [[50 parts per hour - (400 parts / (8 hours + 6.67 hours))]].

Therefore, the productivity of the first worker is [[50 parts per hour - (400 parts / 14.67 hours)]].

Let's calculate the productivity of the first worker:

Total productivity = 400 parts / 8 hours = 50 parts per hour

Time taken by the second worker = 8 hours + 6.67 hours = 14.67 hours

Productivity of the first worker = 50 parts per hour - (400 parts / 14.67 hours)

Productivity of the first worker = 50 parts per hour - 27.26 parts per hour

Productivity of the first worker = 22.74 parts per hour

Therefore, the productivity of the first worker is 22.74 parts per hour.

Answer

The productivity of the first worker is 22.74 parts per hour.