Question

привезли 360 заготовок для деталей. Мастер может изготовить все детали за 6 дней, его ученик за 12 дней. За сколько дней мастер и ученик могут выполнить все задание, работая вместе?

Answer 1

Problem Analysis

We are given that a master can manufacture all the parts from 360 blanks in 6 days, while his apprentice can do it in 12 days. We need to determine how many days it will take for the master and the apprentice to complete the task together.

Solution

To solve this problem, we can use the concept of work rates. The work rate is defined as the amount of work done per unit of time. In this case, we can consider the work rate as the number of parts manufactured per day.

Let's denote the work rate of the master as M (parts per day) and the work rate of the apprentice as A (parts per day). We are given that the master can manufacture all the parts in 6 days, so we can calculate the master's work rate as:

M = 360 parts / 6 days = 60 parts per day.

Similarly, we are given that the apprentice can manufacture all the parts in 12 days, so we can calculate the apprentice's work rate as:

A = 360 parts / 12 days = 30 parts per day.

Now, let's consider the scenario where the master and the apprentice work together. In this case, their work rates will add up. So the combined work rate of the master and the apprentice working together is:

M + A = 60 parts per day + 30 parts per day = 90 parts per day.

To determine how many days it will take for the master and the apprentice to complete the task together, we can divide the total number of parts (360) by their combined work rate (90 parts per day):

Number of days = Total number of parts / Combined work rate = 360 parts / 90 parts per day = 4 days.

Therefore, it will take the master and the apprentice 4 days to complete the task together.

Answer

The master and the apprentice can complete all the parts in 4 days if they work together.