Question

Мастер изготовляет на 8 деталей в час больше, чем ученик. Ученик работал 6 часов, мастер – 8 часов, и вместе они изготовили 232 детали. Сколько деталей в час изготовлял ученик?

Answer 1

X------деталей изготавливал ученик
x+8----деталей изготавливал мастер
6x+8(x+8)=232
6x+8x+64=232
14x=168
x=168:14
x=12 деталей в час изготовлял ученик

Answer 2

Problem Analysis

We are given that a master produces 8 parts per hour more than an apprentice. The apprentice worked for 6 hours, the master worked for 8 hours, and together they produced a total of 232 parts. We need to determine how many parts per hour the apprentice produced.

Solution

Let's assume that the apprentice produces x parts per hour. Since the master produces 8 parts per hour more than the apprentice, the master produces (x + 8) parts per hour.

The total number of parts produced by the apprentice in 6 hours is 6x, and the total number of parts produced by the master in 8 hours is 8(x + 8). The sum of these two quantities is equal to 232:

6x + 8(x + 8) = 232

Simplifying the equation:

6x + 8x + 64 = 232 14x + 64 = 232 14x = 232 - 64 14x = 168 x = 168 / 14 x = 12

Therefore, the apprentice produced 12 parts per hour.

Answer

The apprentice produced 12 parts per hour.

Verification

Let's verify the solution by substituting the value of x back into the equation:

6x + 8(x + 8) = 232 6(12) + 8(12 + 8) = 232 72 + 8(20) = 232 72 + 160 = 232 232 = 232

The equation holds true, confirming that the apprentice produced 12 parts per hour.