Question

В мастерской мастер выполняет на 5 деталей в час больше,чем ученик.Найдите производительности труда мастера и ученика,если известно,что дневную норму,равную 160 деталям,мастер выполняет на 1 час 36 минут быстрее,чем ученик.

Answer 1

Ученик - 20 деталей, мастер - 25 деталей.
Решение такое:
Пусть ученик делает в час х деталей, х+5 деталей; 1 час 36 мин = 1,6 часа.
Составим уравнение:
160\х - 160\(х+5) = 1,6
160х+800-160х-1,6х² - 8х=0
х² +5х-500=0
х=20.
Ответ: 20 деталей, 25 деталей.

Answer 2

Calculation of Labor Productivity

To find the labor productivity of the master and the apprentice, we need to determine the number of parts each of them can produce in one hour.

Given the information provided: - The master completes 5 parts per hour more than the apprentice. - The master completes the daily norm of 160 parts in 1 hour and 36 minutes faster than the apprentice.

Let's calculate the labor productivity of the master and the apprentice:

1. Convert the time difference between the master and the apprentice's completion of the daily norm into minutes: - 1 hour and 36 minutes = 60 minutes + 36 minutes = 96 minutes.

2. Calculate the labor productivity of the apprentice: - If the master completes the daily norm of 160 parts in 96 minutes faster than the apprentice, the apprentice takes 96 minutes longer to complete the daily norm. - Therefore, the apprentice completes the daily norm in 24 hours + 96 minutes = 24 hours and 96 minutes = 1440 minutes + 96 minutes = 1536 minutes. - The labor productivity of the apprentice is calculated by dividing the daily norm of 160 parts by the time taken to complete it, which is 1536 minutes: - Apprentice's labor productivity = 160 parts / 1536 minutes = 0.1042 parts per minute.

3. Calculate the labor productivity of the master: - Since the master completes 5 parts per hour more than the apprentice, the master completes the daily norm of 160 parts in 24 hours - 1 hour = 23 hours. - The time taken by the master to complete the daily norm is 23 hours + 96 minutes = 23 hours and 96 minutes = 1380 minutes + 96 minutes = 1476 minutes. - The labor productivity of the master is calculated by dividing the daily norm of 160 parts by the time taken to complete it, which is 1476 minutes: - Master's labor productivity = 160 parts / 1476 minutes = 0.1084 parts per minute.

Therefore, the labor productivity of the master is 0.1084 parts per minute, and the labor productivity of the apprentice is 0.1042 parts per minute.