Question

При совместной работе мастер иего ученик за 2 часа работы могут обрабатывать 24 детали . за какое время при созранении той же производительности сможет обработать эти 24 детали один ученик,если производительность мастера на 6 деталей в час выше, чем производительность ученика?

Answer 1

24-6*2=12            12:2=6             24: 6=4(часа )-это ответ

Answer 2

Problem Analysis

The problem states that a master and his apprentice can process 24 parts in 2 hours. We need to find out how long it would take for the apprentice to process the same 24 parts if the master's productivity is 6 parts per hour higher than the apprentice's.

Solution

Let's denote the master's productivity as M parts per hour and the apprentice's productivity as A parts per hour. We are given that M = A + 6, and we need to find the time it takes for the apprentice to process 24 parts.

The combined productivity of the master and the apprentice is 24 parts in 2 hours. We can use this information to form an equation and solve for the time it takes for the apprentice to process 24 parts alone.

Calculations

Let's denote the time it takes for the apprentice to process 24 parts as T hours. Using the given information, we can set up the equation:

2(M + A) = 24

Substitute M = A + 6: 2(A + 6 + A) = 24 2(2A + 6) = 24 4A + 12 = 24 4A = 24 - 12 4A = 12 A = 3

So, the apprentice's productivity is 3 parts per hour. Now we can find the time it takes for the apprentice to process 24 parts: 24 = 3T T = 24 / 3 T = 8

Answer

The apprentice, working alone, would be able to process the 24 parts in 8 hours while maintaining the same productivity as before.