Question

Первый мастеп модеи выполнить задание за 4 ч, второй мастер-за 5 ч. Третий масиер может выполнить за 1 ч на 0,1 задания больше, чем второй. Какая часть задания останется невыполненной, если три мастера будут работать совместно 1 ч?

Answer 1

1/4 часть - первый мастер за 1 час
1/5 часть - второй за 1 час
1/5+1/10=3/10 части - третий за 1 час

1/4+1/5+3/10=5/20+4/20+6/20=15/20=3/4(части) - сделают вместе за 1 час

Answer 2

Problem Analysis

We are given three masters who are working on a task. The first master can complete the task in 4 hours, the second master can complete it in 5 hours, and the third master can complete 0.1 more of the task than the second master in 1 hour. We need to determine how much of the task will remain unfinished if all three masters work together for 1 hour.

Solution

To solve this problem, we can calculate the combined work rate of the three masters and then determine how much of the task they can complete in 1 hour.

Let's denote the amount of work completed by the first master in 1 hour as x. Since the first master can complete the task in 4 hours, their work rate is 1/4 of the task per hour.

The second master can complete the task in 5 hours, so their work rate is 1/5 of the task per hour.

The third master can complete 0.1 more of the task than the second master in 1 hour. Let's denote the amount of work completed by the third master in 1 hour as y. Since the third master can complete 0.1 more of the task than the second master, their work rate is (1/5 + 0.1) of the task per hour.

Now, we can calculate the combined work rate of the three masters by adding their individual work rates:

Combined work rate = 1/4 + 1/5 + (1/5 + 0.1)

To find the amount of work completed by the three masters in 1 hour, we multiply the combined work rate by 1:

Amount of work completed in 1 hour = (1/4 + 1/5 + (1/5 + 0.1)) * 1

To determine the amount of work that will remain unfinished after 1 hour, we subtract the amount of work completed in 1 hour from the total task:

Amount of work remaining = 1 - (1/4 + 1/5 + (1/5 + 0.1)) * 1

Let's calculate the result:

Amount of work remaining = 1 - (1/4 + 1/5 + (1/5 + 0.1)) * 1

Amount of work remaining = 0.45

Therefore, if the three masters work together for 1 hour, 0.45 of the task will remain unfinished.