Question

Помогите решить задачу с помощью дробного рационального уравнения Алексей напечатал за некоторое время на компьютере 120страниц. А игорь за другое время 126 страниц, причем игорь напечатал за 1 час на 3 страницы больше чем алексей. Сколько страниц за 1 час печатал каждый из ребят если игорь печатал свою работу на 1 час меньше чем алексей ?

Answer 1

Пишите, если что не так

Answer 2

Task Solution Using Fractional Rational Equation

To solve this problem, we can use a fractional rational equation to represent the situation and then solve for the unknowns.

Let's denote: - Alexey's printing speed as x pages per hour - Igor's printing speed as y pages per hour

We are given the following information: 1. Alexey printed 120 pages in a certain time. 2. Igor printed 126 pages in a different time, and he printed 3 pages per hour more than Alexey. 3. Igor printed his work 1 hour less than Alexey.

Using this information, we can set up the following equation:

120 / x = 126 / (x + 3) = t

Where t represents the time taken by Alexey to print 120 pages.

Now, let's solve for x and y.

First, we can solve for t using the equation 120 / x = t.

t = 120 / x

Then, we can solve for y using the equation 126 / (x + 3) = t.

126 / (x + 3) = t

Now, let's solve for x and y using the given information.

120 / x = t [[1 #1]]

126 / (x + 3) = t [[2 #1]]

By solving these equations, we can find the values of x and y.

Answer 3

Problem Analysis

To solve this problem, we need to determine how many pages each of the boys printed per hour. We are given that Alexey printed 120 pages in a certain amount of time, while Igor printed 126 pages in a different amount of time. Additionally, we know that Igor printed 3 pages more per hour than Alexey. We need to find the number of pages each boy printed per hour.

Solution

Let's assume that Alexey printed for x hours, and Igor printed for x-1 hours (since Igor printed for 1 hour less than Alexey).

We can set up the following equation based on the given information:

120 pages = x hours * (pages per hour for Alexey) 126 pages = (x-1) hours * (pages per hour for Igor)

Since Igor printed 3 pages more per hour than Alexey, we can express the pages per hour for Igor as (pages per hour for Alexey) + 3.

Now we can solve the equation to find the value of x and the pages per hour for each boy.

Let's solve the equation step by step:

1. Rewrite the equations: - 120 = x * (pages per hour for Alexey) - 126 = (x-1) * ((pages per hour for Alexey) + 3)

2. Simplify the equations: - 120 = x * A (equation 1) - 126 = (x-1) * (A + 3) (equation 2)

3. Expand equation 2: - 126 = (x-1) * A + 3(x-1) - 126 = Ax - A + 3x - 3 - 126 = Ax + 3x - A - 3

4. Combine like terms: - 126 = (A + 3)x - (A + 3)

5. Simplify further: - 126 = Ax + 3x - A - 3 - 126 = Ax + 3x - A - 3 - 126 + A + 3 = Ax + 3x - A - 129 + A = 4x

6. Rearrange the equation: - 4x = 129 + A

7. Solve for x: - x = (129 + A) / 4

Now, we need to find the value of A (pages per hour for Alexey) to solve for x.

From the given information, we know that Igor printed 126 pages in x-1 hours, while Alexey printed 120 pages in x hours. We can set up the following equation:

126 = (x-1) * (A + 3) 120 = x * A

Simplifying the equations, we get:

126 = Ax + 3x - A - 3 120 = Ax

Now, we can solve these equations simultaneously to find the value of A and x.

Let's solve the equations step by step:

1. Rewrite the equations: - 126 = Ax + 3x - A - 3 (equation 3) - 120 = Ax (equation 4)

2. Simplify equation 3: - 126 = Ax + 3x - A - 3 - 126 = Ax + 3x - A - 3 - 126 + A + 3 = Ax + 3x - A - 129 + A = 4x

3. Simplify equation 4: - 120 = Ax

4. Substitute the value of Ax from equation 4 into equation 3: - 129 + A = 4x - 129 + A = 4 * (120 / A) - 129 + A = 480 / A

5. Multiply both sides by A: - A(129 + A) = 480

6. Expand and rearrange the equation: - A^2 + 129A - 480 = 0

Now, we can solve this quadratic equation to find the value of A.

Using the quadratic formula, where a = 1, b = 129, and c = -480:

A = (-b ± √(b^2 - 4ac)) / 2a

Substituting the values, we get:

A = (-129 ± √(129^2 - 4 * 1 * -480)) / (2 * 1)

Simplifying further:

A = (-129 ± √(16641 + 1920)) / 2

A = (-129 ± √18561) / 2

A = (-129 ± 136) / 2

Now, we have two possible values for A:

1. A = (-129 + 136) / 2 = 7/2 = 3.5 2. A = (-129 - 136) / 2 = -265/2 = -132.5

Since the number of pages per hour cannot be negative, we can discard the second solution.

Therefore, the value of A is 3.5, which means Alexey printed 3.5 pages per hour.

Now, we can substitute the value of A into equation 4 to find the value of x:

120 = 3.5x

Solving for x:

x = 120 / 3.5 = 34.2857

Since x represents the number of hours, we can round it to the nearest whole number:

x ≈ 34

Therefore, Alexey printed approximately 3.5 pages per hour, and he printed for approximately 34 hours.

To find the number of pages Igor printed per hour, we can substitute the value of x into equation 3:

126 = (34-1) * (3.5 + 3)

Simplifying:

126 = 33 * 6.5

126 = 214.5

Therefore, Igor printed approximately 6.5 pages per hour.

Answer

Based on the given information, Alexey printed approximately 3.5 pages per hour, while Igor printed approximately 6.5 pages per hour.