Question

Одна бригада может выполнить задание за 10 часов, а вторая -за 15 часов. Сначала первая бригада отработала 2 часов, а затем вторая бригада - 6 часов. После чего обе бригады выполнили оставшуюся часть работы. За какое время это произошло? (Время выразите в часах и минутах)

Answer 1

За шесть дней это прошло

Answer 2

Problem Analysis

We are given that one team can complete a task in 10 hours and another team can complete the same task in 15 hours. The first team worked for 2 hours and the second team worked for 6 hours before both teams completed the remaining work. We need to find out how much time it took for both teams to complete the remaining work.

Solution

Let's assume that the total work to be done is 1 unit.

The first team can complete the work in 10 hours, so their work rate is 1/10 unit per hour.

The second team can complete the work in 15 hours, so their work rate is 1/15 unit per hour.

When the first team worked for 2 hours, they completed 2/10 = 1/5 of the work.

When the second team worked for 6 hours, they completed 6/15 = 2/5 of the work.

So, the total work completed by both teams is 1/5 + 2/5 = 3/5 of the work.

The remaining work is 1 - 3/5 = 2/5 of the work.

Now, we need to find out how much time it will take for both teams to complete the remaining work together.

Let's assume that it takes x hours for both teams to complete the remaining work together.

The work rate of the first team is 1/10 unit per hour and the work rate of the second team is 1/15 unit per hour.

When both teams work together, their combined work rate is 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6 unit per hour.

We can use the formula work = rate × time to find the time it takes to complete the remaining work:

2/5 = (1/6) × x

To solve for x, we can multiply both sides of the equation by 6:

2/5 × 6 = x

Simplifying the equation:

12/5 = x

So, it takes 12/5 hours for both teams to complete the remaining work.

Converting the time to hours and minutes:

12/5 hours = 2 hours and 24 minutes

Therefore, it took both teams 2 hours and 24 minutes to complete the remaining work.

Answer

It took both teams 2 hours and 24 minutes to complete the remaining work.