Question

токарь может обточить 72 заготовки за 3 часа, а его ученику на выполнение той же работы требуется в 2 раза больше времени.За сколько часов они обточат 144 такие же заготовки при совместной работе?

Answer 1

1)3*2=6ч понадобится ученику

2)72:3=24заготовки в час делает токарь

3)72:6=12 заготовок в час делает ученик

4)24+12=36 заготовок они сделают вместе за час

5)144:36=4ч понадобится им что бы съделать 144 заготовки

Answer 2

Problem Analysis

We are given that a lathe operator can machine 72 workpieces in 3 hours, while his apprentice takes twice as long to complete the same task. We need to determine how long it will take them to machine 144 workpieces if they work together.

Solution

Let's start by finding the individual rates at which the lathe operator and the apprentice can machine workpieces.

The lathe operator can machine 72 workpieces in 3 hours, so his rate is 72 workpieces / 3 hours = 24 workpieces per hour.

The apprentice takes twice as long as the lathe operator, so his rate is half of the lathe operator's rate: 24 workpieces per hour / 2 = 12 workpieces per hour.

Now, let's calculate how long it will take them to machine 144 workpieces if they work together.

Let's assume that it takes them x hours to machine 144 workpieces when working together.

The combined rate of the lathe operator and the apprentice is the sum of their individual rates: 24 workpieces per hour + 12 workpieces per hour = 36 workpieces per hour.

Using the formula rate = work / time, we can write the equation:

36 workpieces per hour = 144 workpieces / x hours.

To solve for x, we can cross-multiply and solve for x:

36x = 144.

Dividing both sides of the equation by 36, we get:

x = 144 / 36 = 4.

Therefore, it will take them 4 hours to machine 144 workpieces when working together.

Answer

If the lathe operator and his apprentice work together, they will be able to machine 144 workpieces in 4 hours.