Question

Две наборщицы должны были набрать по 120 страниц каждая. Вторая наборщица набирала за 1 час на 5 страниц меньше, чем первая, поэтому закончила работу на 2 часа позже. Сколько страниц в час набирала первая наборшица?

Answer 1

Ответ:

х+у=120

у=5+х

2х+5=120

у=5+х

х=57,5

у=62,5

Ответ: 62,5 стр

Answer 2

Problem Analysis

We are given that two typists had to type 120 pages each. The second typist typed 5 pages less per hour than the first typist and finished the work 2 hours later. We need to find out how many pages per hour the first typist typed.

Solution

Let's assume that the first typist typed at a rate of x pages per hour. Since the second typist typed 5 pages less per hour, their rate would be x - 5 pages per hour.

We know that the first typist finished their work in the same amount of time it took the second typist plus 2 hours. So, the time taken by the first typist is t hours, and the time taken by the second typist is t + 2 hours.

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

120 / x = (120 / (x - 5)) + 2

To solve this equation, we can multiply both sides by x(x - 5) to eliminate the denominators:

120(x - 5) = 120x + 2x(x - 5)

Simplifying the equation:

120x - 600 = 120x + 2x^2 - 10x

Combining like terms:

2x^2 - 10x - 600 = 0

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

Quadratic Equation Solution

Using the quadratic formula, x = (-b ± √(b^2 - 4ac)) / (2a), where a = 2, b = -10, and c = -600:

x = (-(-10) ± √((-10)^2 - 4 * 2 * -600)) / (2 * 2)

Simplifying:

x = (10 ± √(100 + 4800)) / 4

x = (10 ± √4900) / 4

x = (10 ± 70) / 4

So, we have two possible solutions for x:

x1 = (10 + 70) / 4 = 80 / 4 = 20

x2 = (10 - 70) / 4 = -60 / 4 = -15

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

Therefore, the first typist typed at a rate of 20 pages per hour.

Answer

The first typist typed at a rate of 20 pages per hour.