Question

мастер изготавливает 24 детали на час быстрее, чем ученик изготавливает 20 деталей. За сколько часов мастер и ученик, работая вместе, изготовят 70, если известно, что за один час мастер изготавливает на 2 детали больше, чем ученик?

Answer 1

Ответ: 7 часов

Объяснение:

Answer 2

Problem Analysis

We are given that a master can produce 24 parts per hour, which is 4 parts faster than an apprentice who can produce 20 parts per hour. We need to determine how many hours it will take for the master and apprentice to produce a total of 70 parts, considering that the master produces 2 more parts per hour than the apprentice.

Solution

Let's assume it takes the master x hours to produce 70 parts. Since the master produces 24 parts per hour, the total number of parts produced by the master in x hours is 24x.

Similarly, let's assume it takes the apprentice y hours to produce 70 parts. Since the apprentice produces 20 parts per hour, the total number of parts produced by the apprentice in y hours is 20y.

According to the given information, the master produces 2 more parts per hour than the apprentice. So, we can write the equation:

24x = 20y + 2y

Simplifying the equation:

24x = 22y

To find the values of x and y, we need to find a common multiple of 24 and 22. The least common multiple (LCM) of 24 and 22 is 264.

Dividing both sides of the equation by the common multiple:

x = (22y) / 24

Simplifying further:

x = (11y) / 12

Since x and y represent the number of hours, they must be integers. To find the smallest integer value of y that satisfies the equation, we can substitute different values of y and check if x is an integer.

Let's substitute y = 12:

x = (11 * 12) / 12 = 11

So, it will take the master and apprentice 11 hours to produce a total of 70 parts.

Answer

The master and apprentice, working together, will take 11 hours to produce a total of 70 parts.