Question

Один рабочий может выполнить производственное задание за 5 часов, а другой за 15 часов. Какую часть задания они выпалнят , если будут работать вместе 1 1/4 часа? Успеют ли они , работая вместе выполнить задание за 3 часа

Answer 1

1 - выполняет 1 за 5 часов
1/3 - выполняет 2 за 5 часов
1:5*1 1/4=1/5*5/4=5/20 выполнит первый за 1 1/4 часа
1/3:5*1 1/4=1/15*1 1/4=5/60
5/20+5/60=(15+5)/60=20/60=1/3 выполнят задания 2 рабочих работая вместе 1 1/4 часа
1/5*3=3/5 выполнит 1 за 3 часа
1/3:5*3=1/15*3=3/15 выполнит 2 за 3 часа
3/5+3/15=9/15+3/15=12/15=4/5 выполнят задания 2 рабочих работая вместе 3 часа, нет не успеют

Answer 2

Problem Analysis

We have two workers who can complete a production task in 5 hours and 15 hours, respectively. We need to determine what portion of the task they will complete if they work together for 1 1/4 hours. Additionally, we need to determine if they will be able to complete the task in 3 hours if they work together.

Calculation

To find out what portion of the task the workers will complete when working together for 1 1/4 hours, we can calculate their combined work rate. Let's denote the work rate of the first worker as W1 (in units of task per hour) and the work rate of the second worker as W2 (in units of task per hour).

The work rate of the first worker is 1 task per 5 hours, which can be expressed as W1 = 1/5 task per hour.

The work rate of the second worker is 1 task per 15 hours, which can be expressed as W2 = 1/15 task per hour.

To find their combined work rate, we can add their individual work rates: W_combined = W1 + W2.

Now, we need to calculate the work done by the workers when they work together for 1 1/4 hours. The total work done is equal to the combined work rate multiplied by the time worked: Work_done = W_combined * Time_worked.

Substituting the values, we have Work_done = (W1 + W2) * 1 1/4.

To determine if they will be able to complete the task in 3 hours when working together, we can calculate the work done in 3 hours using the same formula: Work_done_3_hours = (W1 + W2) * 3.

Calculation Results

Let's calculate the results using the given information:

- Worker 1's work rate: W1 = 1/5 task per hour - Worker 2's work rate: W2 = 1/15 task per hour - Combined work rate: W_combined = W1 + W2 - Work done in 1 1/4 hours: Work_done = W_combined * 1 1/4 - Work done in 3 hours: Work_done_3_hours = W_combined * 3

Calculation Results

Let's calculate the results using the given information:

- Worker 1's work rate: W1 = 1/5 task per hour - Worker 2's work rate: W2 = 1/15 task per hour - Combined work rate: W_combined = W1 + W2 - Work done in 1 1/4 hours: Work_done = W_combined * 1 1/4 - Work done in 3 hours: Work_done_3_hours = W_combined * 3

Now, let's calculate the values:

- Worker 1's work rate: W1 = 1/5 task per hour - Worker 2's work rate: W2 = 1/15 task per hour - Combined work rate: W_combined = W1 + W2 = 1/5 + 1/15 = 4/15 task per hour

To find the work done in 1 1/4 hours, we multiply the combined work rate by the time worked:

- Work done in 1 1/4 hours: Work_done = W_combined * 1 1/4 = (4/15) * (5/4) = 1/3 task

To find the work done in 3 hours, we multiply the combined work rate by the time worked:

- Work done in 3 hours: Work_done_3_hours = W_combined * 3 = (4/15) * 3 = 4/5 task

Answer

Therefore, if the two workers work together for 1 1/4 hours, they will complete 1/3 of the task. However, if they work together for 3 hours, they will be able to complete 4/5 of the task.

Please let me know if there's anything else I can help you with!