Question

на изготовление 252 деталей первый рабочий затрачивает на 9 часов меньше,чем второй рабочий на изготовление 420 деталей. известно, что первый рабочий за час делает на 1 деталь больше, чем второй.сколько деталей в час делает первый рабочий?

Answer 1

Пусть первый рабочий делает х деталей в час, а второй рабочий делает у деталей в час. Составляем уравнения:

252/x + 9 = 420/y

x = y + 1

Подставляем и решаем:

252/(y + 1) + 9 = 420/y

у = 20

х = 21

Ответ: 21 деталь в час. 

Answer 2

Problem Analysis

We are given that the first worker takes 9 hours less than the second worker to manufacture 252 parts. Additionally, the first worker can make 1 more part per hour than the second worker. We need to determine how many parts the first worker can make in one hour.

Solution

Let's assume that the second worker can make x parts in one hour. Therefore, the first worker can make (x + 1) parts in one hour.

We know that the first worker takes 9 hours less than the second worker to manufacture 252 parts. This means that the second worker takes x hours to manufacture 252 parts, while the first worker takes (x - 9) hours to manufacture the same number of parts.

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

(x - 9) * (x + 1) = 252

Simplifying the equation:

x^2 - 8x - 243 = 0

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

Using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = -8, and c = -243.

Calculating the discriminant:

D = b^2 - 4ac = (-8)^2 - 4(1)(-243) = 64 + 972 = 1036

Since the discriminant is positive, we have two real solutions for x.

Using the quadratic formula:

x = (-(-8) ± √(1036)) / (2 * 1) x = (8 ± √(1036)) / 2 x = (8 ± √(4 * 259)) / 2 x = (8 ± 2√259) / 2 x = 4 ± √259

Since the number of parts cannot be negative, we can ignore the negative solution.

Therefore, the second worker can make 4 + √259 parts in one hour.

To find the number of parts the first worker can make in one hour, we add 1 to the second worker's rate:

First worker's rate = (4 + √259) + 1 = 5 + √259

Hence, the first worker can make 5 + √259 parts in one hour.

Answer

The first worker can make 5 + √259 parts in one hour.