Question

Робітник може виконати завдання за 2 год, а його учень за 5 год. Чи виконають вони 2/3 завдання за 1 год спільної роботи?

Answer 1

Ответ:

Приймемо всю роботу за 1. Тоді за 1 год перший робітник виконає 1/5 частину роботи, а другий - 1/15 частину. За 1 год вони виконають

1/5 + 1/15 = 4/15 частини роботи.

За 1 1/4 год робітники виконають 1 1/4 • 4/15= 1/3 частину роботи. За 3 год вони виконають 3 • 4/15 = 4/5 частини роботи.

Відповідь. За 1 1/4 год робітники виконають 1/3 частину роботи; за 3 год вони не встигнуть виконати замовлення.

Answer 2

Task Completion Time

To determine if the worker and their student can complete 2/3 of the task in 1 hour of joint work, we need to calculate their combined work rate.

Let's assume that the worker's work rate is 1 task per 2 hours, and the student's work rate is 1 task per 5 hours.

The worker's work rate can be expressed as 1/2 task per hour, and the student's work rate can be expressed as 1/5 task per hour.

To find their combined work rate, we can add their individual work rates:

1/2 task per hour + 1/5 task per hour = 5/10 + 2/10 = 7/10 task per hour.

Therefore, their combined work rate is 7/10 task per hour.

Task Completion in 1 Hour

Now, let's calculate how much of the task they can complete in 1 hour of joint work.

Since their combined work rate is 7/10 task per hour, they can complete 7/10 of the task in 1 hour.

However, we need to determine if they can complete 2/3 of the task in 1 hour.

To compare these values, we can convert 2/3 to a decimal:

2/3 = 0.6667 (rounded to four decimal places).

Comparing 0.6667 to 7/10, we can see that 7/10 is greater than 0.6667.

Therefore, the worker and their student can indeed complete more than 2/3 of the task in 1 hour of joint work.

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