Question

Мастер может изготовить 540 деталей за 9 дней, а его ученик за 18 дней. За сколько дней мастер и ученик из готовят деталей работая вместе

Answer 1

540/9=60
540/18=30
60+30=90
540/90=6 дней

Answer 2

1) 540:9=60 деталей за 1 день изготовит мастер
2) 540:18=30 деталей за 1 день изготовит ученик
3) 60+30=90 деталей за 1 день изготовят мастер и ученик
4) 540:90= за 6 дней изготовят вместе

Answer 3

Problem Analysis

We are given that a master can manufacture 540 parts in 9 days, while their apprentice can manufacture the same number of parts in 18 days. We need to determine how many days it will take for the master and the apprentice to manufacture the parts 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, the work rate is 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 540 parts in 9 days, so we can calculate the master's work rate as:

M = 540 parts / 9 days = 60 parts per day.

Similarly, we are given that the apprentice can manufacture 540 parts in 18 days, so the apprentice's work rate is:

A = 540 parts / 18 days = 30 parts per day.

To find the combined work rate of the master and the apprentice, we can add their individual work rates:

Combined work rate = M + A = 60 parts per day + 30 parts per day = 90 parts per day.

Finally, to determine how many days it will take for the master and the apprentice to manufacture the parts together, we can divide the total number of parts (540) by the combined work rate (90 parts per day):

Number of days = Total number of parts / Combined work rate = 540 parts / 90 parts per day = 6 days.

Therefore, it will take the master and the apprentice 6 days to manufacture the parts together.

Answer

The master and the apprentice will manufacture the parts together in 6 days.

Verification

Let's verify the answer using the given information. We know that the master can manufacture 540 parts in 9 days, which means their daily work rate is 60 parts per day. Similarly, the apprentice can manufacture 540 parts in 18 days, which means their daily work rate is 30 parts per day.

If we add their individual work rates, we get a combined work rate of 90 parts per day. Multiplying this combined work rate by the number of days, we should get the total number of parts manufactured:

Combined work rate * Number of days = 90 parts per day * 6 days = 540 parts.

This matches the total number of parts given in the problem, so our answer is verified.