Question

Каждый из двух рабочих одинаковой квалификации может выполнить заказ за 15 часов. Через 3 часа после того, как один из них приступил к выполнению заказа, к нему присоединился второй рабочий, и работу над заказом они довели до конца уже вместе. Сколько часов потребовалось на выполнение всего заказа?

Answer 1

15ч - всего времени на задачу

3 уже работал другой

15-3=12

12/2=6 это работали вместе часов

6+3=9 часов

ответ 9 часов понадобиться

Answer 2

Problem Analysis

We are given that two workers of the same qualification can complete an order in 15 hours. One of the workers started working on the order and after 3 hours, the second worker joined. Together, they completed the order. We need to determine how many hours it took to complete the entire order.

Solution

Let's assume that the rate of work for each worker is x. Since both workers have the same qualification, their rates of work are equal.

According to the given information, one worker can complete the order in 15 hours. Therefore, the rate of work for one worker is 1/15 orders per hour.

After 3 hours, the first worker completed 3 * (1/15) = 1/5 of the order.

When the second worker joined, both workers worked together to complete the remaining 4/5 of the order.

Let's assume it took t hours for both workers to complete the remaining 4/5 of the order.

The combined rate of work for both workers is 2x (since they are working together).

According to the given information, the combined rate of work for both workers is equal to the rate of work for one worker, which is 1/15 orders per hour.

Therefore, we can set up the following equation:

2x * t = 4/5

Simplifying the equation, we get:

2xt = 4/5

Now, we need to solve for t.

Let's solve the equation:

2xt = 4/5

t = (4/5) / (2x)

Since we know that x = 1/15, we can substitute this value into the equation:

t = (4/5) / (2 * (1/15))

Simplifying further, we get:

t = (4/5) / (2/15) = (4/5) * (15/2) = 12

Therefore, it took 12 hours for both workers to complete the remaining 4/5 of the order.

To find the total time taken to complete the entire order, we add the time taken by the first worker (3 hours) to the time taken by both workers to complete the remaining 4/5 of the order (12 hours):

Total time = 3 + 12 = 15 hours

Therefore, it took 15 hours to complete the entire order.

Answer

It took 15 hours to complete the entire order.