Question

За 3 часа машинистка напечатала m страниц, а другая за 5 часов n страниц. Сколько всего страниц напечатают обе машинистки за 15 часов? вычислить при m=20 и n=30. И составьте буквенную запись, пожалуйста

Answer 1

210 страниц напечатают обе машинистки

Answer 2

Problem Analysis

We are given that one typist can type m pages in 3 hours, and another typist can type n pages in 5 hours. We need to find the total number of pages both typists can type in 15 hours.

Solution

To find the total number of pages both typists can type in 15 hours, we need to calculate the number of pages each typist can type per hour and then multiply it by the total number of hours.

Let's calculate the number of pages each typist can type per hour:

- The first typist can type m pages in 3 hours. Therefore, the number of pages the first typist can type per hour is m/3. - The second typist can type n pages in 5 hours. Therefore, the number of pages the second typist can type per hour is n/5.

Now, let's calculate the total number of pages both typists can type in 15 hours:

- The first typist can type m/3 pages per hour. Therefore, in 15 hours, the first typist can type (m/3) * 15 pages. - The second typist can type n/5 pages per hour. Therefore, in 15 hours, the second typist can type (n/5) * 15 pages.

To find the total number of pages both typists can type in 15 hours, we add the number of pages typed by each typist:

Total number of pages = (m/3) * 15 + (n/5) * 15

Now, let's substitute the given values m = 20 and n = 30 into the equation:

Total number of pages = (20/3) * 15 + (30/5) * 15

Simplifying the equation:

Total number of pages = (200/3) + (450/5)

To add the fractions, we need to find a common denominator:

Total number of pages = (200/3) + (450/5) = (200/3) + (450/5) * (3/3) = (200/3) + (1350/15)

Now, let's add the fractions:

Total number of pages = (200/3) + (1350/15) = (200/3) + (90/1) = (200/3) + (90/1) * (3/3) = (200/3) + (270/3)

Adding the fractions:

Total number of pages = (200 + 270)/3 = 470/3

Therefore, the total number of pages both typists can type in 15 hours when m = 20 and n = 30 is 470/3 pages.

Answer

The total number of pages both typists can type in 15 hours when m = 20 and n = 30 is 470/3 pages.

Calculation Steps

- The first typist can type m/3 pages per hour, which is 20/3 pages per hour. - The second typist can type n/5 pages per hour, which is 30/5 pages per hour. - In 15 hours, the first typist can type (20/3) * 15 pages. - In 15 hours, the second typist can type (30/5) * 15 pages. - Therefore, the total number of pages both typists can type in 15 hours is (20/3) * 15 + (30/5) * 15 = 470/3 pages.