Question

Токарь может обточить 72 заготовки за 3 ч, а его ученику потребуется в два раза больше времени. За сколько часов они обточат 144 заготовки при совместной работе?

Answer 1

72:3=24дет в час токарь
24:2=12 дет в час ученик
24+12=36дет в час вместе
144:36=4 часа

Answer 2

Problem Analysis

We are given that a turner (tokar) can machine 72 workpieces in 3 hours, while their apprentice takes twice as long. We need to determine how long it will take them to machine 144 workpieces when working together.

Solution

Let's start by finding the time it takes for the apprentice to machine one workpiece. We know that the turner takes 3 hours to machine 72 workpieces, so the turner's rate is 72 workpieces / 3 hours = 24 workpieces per hour.

Since the apprentice takes twice as long as the turner, their rate is half of the turner's rate, which is 24 workpieces per hour / 2 = 12 workpieces per hour.

Now, let's calculate the total time it will take for both the turner and the apprentice to machine 144 workpieces when working together. We can use the formula:

Total time = Total work / Combined rate

The total work is 144 workpieces, and the combined rate is the sum of the turner's rate and the apprentice's rate, which is 24 workpieces per hour + 12 workpieces per hour = 36 workpieces per hour.

Plugging these values into the formula, we get:

Total time = 144 workpieces / 36 workpieces per hour = 4 hours

Therefore, it will take the turner and the apprentice 4 hours to machine 144 workpieces when working together.

Answer

When working together, the turner and the apprentice will machine 144 workpieces in 4 hours.