Question

Один рабочий может выполнить заказ за 6 дней, а другой за 15 дней, сначала работал первый рабочий, а затем закончил работу второй. Заказ был выполнен за 9 дней. Сколько деталей было изготовлено, если первый сделал на 150 деталей больше, чем второй?

Answer 1

Пусть первый работал х дней. тогда он сделал x/6 заказа. второй работал тогда 9-х дней и сделал (9-x):15 заказа. По условию задачи
$\frac{x}{6}+\frac{9-x}{15}=1$
$5x+2(9-x)=30$
$5x+18-2x=30$
$3x=12$
$x=4$
значит первый рабочий работал4 дня и сделал 4/6=2/3 заказа
второй работал 9-4=5 дней и сделал 5/15=1/3 заказа
получается что 2/3-1/3=1/3 заказа это 150 деталей
значит весь заказ 150*3:1=450 деталей
ответ: 450 деталей

Answer 2

Problem Analysis

We are given that one worker can complete an order in 6 days, while another worker can complete the same order in 15 days. The first worker starts working and then the second worker finishes the job. The total time taken to complete the order is 9 days. We need to determine the number of items produced, given that the first worker produced 150 more items than the second worker.

Solution

Let's assume that the first worker produces x items per day. Therefore, the second worker produces x - 150 items per day.

We can calculate the total number of items produced by the first worker in 9 days as 9x.

Similarly, the total number of items produced by the second worker in 9 days is 9(x - 150).

Since the total number of items produced is the sum of the items produced by both workers, we can set up the following equation:

9x + 9(x - 150) = Total number of items

Simplifying the equation:

9x + 9x - 1350 = Total number of items

18x - 1350 = Total number of items

We are given that the total number of items is equal to the number of items produced in 9 days, which is 9(x + x - 150).

Setting up the equation:

18x - 1350 = 9(x + x - 150)

Simplifying further:

18x - 1350 = 18x - 2700

The 18x terms cancel out, leaving us with:

-1350 = -2700

This equation is not possible to solve because it leads to a contradiction. Therefore, there is no solution to this problem.

Conclusion

Based on the given information, it is not possible to determine the number of items produced because the equation leads to a contradiction.