Question

Токарь может обточить 756 заготовки за 7 дней, а его ученику на выполнение той же работы требуется в 2 раза больше времени. Токарь и ученик обточат 972 такие заготовки при совместной работе за дней?

Answer 1

756 ÷7 = 108 (заготовок) -делает токарь за 1 день, значит,  
108 заготовок делает ученик в два дня. 
108 ÷2 = 54 (заготовки) -делает ученик за 1 день.
108 +54=162 (заг.) делают оба за 1 день.
972 ÷162 = 6(дней).
Ответ: за 6 дней.

Answer 2

Problem Analysis

We are given that a turner (tokar) can machine 756 workpieces in 7 days, while his apprentice takes twice as long to complete the same work. We need to determine how many workpieces they can machine together in a certain number of days.

Solution

Let's assume that the turner's daily work rate is represented by x workpieces per day. Since the turner can machine 756 workpieces in 7 days, we can set up the following equation:

x * 7 = 756 Solving this equation, we find that the turner's daily work rate is x = 756 / 7 = 108 workpieces per day.

Since the apprentice takes twice as long to complete the same work, their daily work rate can be represented by x/2 workpieces per day.

Now, let's assume that the turner and the apprentice work together for a certain number of days, represented by d. The total number of workpieces they can machine together can be calculated using the following equation:

(x + x/2) * d = 972 Substituting the value of x into the equation, we have:

(108 + 108/2) * d = 972

Simplifying the equation, we get:

162 * d = 972

Dividing both sides of the equation by 162, we find:

d = 972 / 162 = 6

Therefore, the turner and the apprentice can machine 972 workpieces together in 6 days.

Answer

When working together, the turner and the apprentice can machine 972 workpieces in 6 days.