Question

Мастер изготавливает на 7 деталей в час больше, чем ученик. ученик работал 3 часа, а мастер 2 часа и вместе они изготовили 224 детали. сколько деталей в час изготавливает ученик? Хелп ми плиззз Решите с помощью системы

Answer 1

Х д. - делает мастер за 1 ч
у д. - делает ученик за 1 ч

х-у=7
3х+2у=224

х=7+у
2(7+у)+3у=224

х=7+у
14+2у+3у=224

х=7+у
5у=210

х=7+у
у=42

х=49(д.) - делает мастер за 1 ч
у=42(д.) - ученик за 1 ч

Answer 2

Problem Analysis

We are given that a master can produce 7 more parts per hour than an apprentice. The apprentice worked for 3 hours, and the master worked for 2 hours, and together they produced a total of 224 parts. We need to determine how many parts the apprentice can produce per hour.

Solution

Let's assume that the apprentice can produce x parts per hour. Since the master can produce 7 more parts per hour, the master can produce (x + 7) parts per hour.

According to the given information, the apprentice worked for 3 hours and the master worked for 2 hours. Therefore, the total number of parts produced by the apprentice is 3x, and the total number of parts produced by the master is 2(x + 7).

We are also given that the total number of parts produced by both the apprentice and the master is 224. Therefore, we can write the following equation:

3x + 2(x + 7) = 224

Simplifying the equation:

3x + 2x + 14 = 224 5x + 14 = 224 5x = 224 - 14 5x = 210 x = 210 / 5 x = 42

Therefore, the apprentice can produce 42 parts per hour.

Answer

The apprentice can produce 42 parts per hour.

Explanation

By solving the given problem using the system of equations, we found that the apprentice can produce 42 parts per hour.