Question

Аня и Таня читают одну и ту же книгу.Аня читает за час 42 страницы,а Таня 36. Дети начали читать книгу одновременно и не прерывались, при этом Аня закончила читать на 50 минут раньше.Сколько страниц текста содержит книга? Мне нужно полное решение с вычислениями! Заранее спасибо за решение!

Answer 1

Х страниц содержит книга
за х/42 часов Аня прочитает всю книгу
за х/36 часов Таня прочитает всю книгу
5 минут = 5/6 часа

$\frac{x}{36} - \frac{x}{42} = \frac{5}{6} \\ \\ 7x - 6x = 210$

х = 210 страниц содержит книга

Answer 2

Problem Analysis

Аня reads 42 pages in 1 hour, while Таня reads 36 pages in 1 hour. Аня finishes reading 50 minutes earlier than Таня. We need to find the total number of pages in the book.

Solution

Let's assume the total number of pages in the book is P.

We know that Аня reads 42 pages in 1 hour, so she reads 42/P pages per minute. Similarly, Таня reads 36 pages in 1 hour, so she reads 36/P pages per minute.

Since Аня finishes reading 50 minutes earlier than Таня, we can set up the following equation:

Аня's reading time = Таня's reading time + 50 minutes

To convert the reading time to the number of pages read, we multiply the reading time by the number of pages read per minute.

42 = (36 + 50) * (42/P)

Now we can solve this equation to find the value of P.

Calculation

Let's solve the equation step by step:

42 = (36 + 50) * (42/P)

Simplifying the equation:

42 = 86 * (42/P)

Dividing both sides of the equation by 86:

42/86 = 42/P

Cross-multiplying:

42P = 86 * 42

Dividing both sides of the equation by 42:

P = (86 * 42) / 42

Simplifying:

P = 86

Therefore, the book contains 86 pages.

Answer

The book contains 86 pages.