Question

Мастер и его ученик за 1 час могут изготовить вместе 17 деталей . До обеда мастер проработал 4 часа, а его ученик - 2 часа, и изготовили вместе вместе 54 детали. Сколько деталей изготовил каждый из них за час?

Answer 1

За 2 часа двое изготовили 17*2=34 детали
соответственно мастер за (4-2)=2 часа изготовил 54-34=20 деталей
за 1 час мастер делает 20/2=10 деталей
за 1 час ученик делает 17-10=7 деталей 
ответ: 17,10

Answer 2

Problem Analysis

We are given that a master and his apprentice can together produce 17 parts in 1 hour. The master worked for 4 hours before lunch, and the apprentice worked for 2 hours. Together, they produced a total of 54 parts. We need to determine how many parts each of them can produce in one hour.

Solution

Let's assume that the master can produce x parts per hour, and the apprentice can produce y parts per hour. We can set up the following equations based on the given information:

Equation 1: x + y = 17 (since they can produce 17 parts together in 1 hour) Equation 2: 4x + 2y = 54 (since the master worked for 4 hours and the apprentice worked for 2 hours, producing a total of 54 parts)

To solve this system of equations, we can use substitution or elimination method. Let's use the elimination method:

Multiplying Equation 1 by 2, we get: 2x + 2y = 34

Subtracting Equation 2 from the above equation, we get: (2x + 2y) - (4x + 2y) = 34 - 54 -2x = -20 x = 10

Substituting the value of x into Equation 1, we get: 10 + y = 17 y = 7

Therefore, the master can produce 10 parts per hour and the apprentice can produce 7 parts per hour.

Answer

The master can produce 10 parts per hour, and the apprentice can produce 7 parts per hour.