Question

Решите задачу. Одна машинистка печает страницу за 10 минут, а другая за 8 минут. Они вместе печатали рукопись и вместе закончили работу. Первая машинистка напечатала 25 страниц. Сколько страниц отпечатала вторая машиниста? Решение обязательно.

Answer 1

Первая за минуту печатает $\frac1{10}$ страницы, вторая $\frac18$ страницы. Скорость второй составляет $\frac1{10}:\frac18=\frac8{10}$ от скорости первой. Значит, за то же время она напечатает 8/10 от страниц, напечатанных первой.
$25\cdot\frac8{10}=\frac{200}{10}=20$ страниц напечатала вторая.

Answer 2

Problem Analysis

We are given that one typist can type a page in 10 minutes and another typist can type a page in 8 minutes. They worked together and completed a manuscript. The first typist typed 25 pages. We need to find out how many pages the second typist typed.

Solution

Let's assume the number of pages the second typist typed is x.

The first typist can type a page in 10 minutes, so in 1 minute, she can type 1/10 of a page. The second typist can type a page in 8 minutes, so in 1 minute, she can type 1/8 of a page.

Together, in 1 minute, they can type 1/10 + 1/8 of a page.

According to the problem, the first typist typed 25 pages. So, we can set up the following equation:

25 = (1/10 + 1/8) * t

Where t is the total time they worked together.

To find the value of x, we need to solve this equation.

Solving the Equation

To solve the equation, we can multiply both sides by the least common multiple (LCM) of 10 and 8, which is 40:

25 * 40 = (1/10 + 1/8) * 40 * t

Simplifying the equation:

1000 = 4 + 5t

Subtracting 4 from both sides:

996 = 5t

Dividing both sides by 5:

t = 199.2

So, they worked together for approximately 199.2 minutes.

Now, we can substitute this value of t back into the equation to find the number of pages the second typist typed:

x = (1/8) * t

x = (1/8) * 199.2

x ≈ 24.9

Therefore, the second typist typed approximately 24.9 pages.

Answer

The second typist typed approximately 24.9 pages.