Question

Двум рабочим надо сделать 3600 деталей. Один рабочий может сделать эти детали за 20 часов, а оба могут сделать за 12 часов. За сколько часов все детали может сделать второй рабочий?

Answer 1

3600:20= 180 lдеталей делает 1 рабочий за 1 час
3600:12=300 деталей вдвоем за 1 час
300 - 180 =120 деталей делает 2 рабочий за 1 час
300:120=30 часов нужно второму для изготовления 3600 деталей

Answer 2

Problem Analysis

We have two workers who need to make 3600 parts. Worker A can make these parts in 20 hours, and both workers together can make them in 12 hours. We need to determine how long it will take for Worker B to make all the parts.

Solution

Let's assume that Worker B can make all the parts in x hours.

From the given information, we know that: - Worker A can make 3600 parts in 20 hours. - Both workers together can make 3600 parts in 12 hours.

Using this information, we can set up the following equations:

Equation 1: Worker A's productivity: 1 part / 20 hours. Equation 2: Both workers' combined productivity: 1 part / 12 hours. Equation 3: Worker B's productivity: 1 part / x hours.

Since we know that the combined productivity of both workers is the sum of their individual productivities, we can write the equation:

1/20 + 1/x = 1/12.

To solve this equation for x, we can multiply both sides by the least common multiple (LCM) of the denominators (20, x, and 12), which is 60x:

3x + 60 = 5x.

Simplifying the equation, we get:

2x = 60.

Dividing both sides by 2, we find:

x = 30.

Therefore, it will take Worker B 30 hours to make all the parts.

Answer

Worker B can make all the 3600 parts in 30 hours.

Verification

Let's verify our answer using the given information.

- Worker A can make 3600 parts in 20 hours, which means their productivity is 1 part per 20 hours. - Both workers together can make 3600 parts in 12 hours, which means their combined productivity is 1 part per 12 hours.

If we substitute the values into the equation, we get:

1/20 + 1/30 = 1/12.

Simplifying the equation, we get:

3/60 + 2/60 = 5/60.

Both sides of the equation are equal, so our answer is verified.

Conclusion

Worker B can make all the 3600 parts in 30 hours.