Question

На изготовление 384 деталей первый рабочий тратит на 8 часов меньше, чем второй рабочий на изготовление 480 таких же деталей. Известно, что первый рабочий за час делает на 4 детали больше, чем второй. Сколько деталей в час делает первый рабочий?

Answer 1

1 рабочий делает x дет. в час, 2 рабочий делает x-4 дет. в час.
384/x + 8 = 480/(x-4)
Делим все на 8
48/x + 1 = 60/(x-4)
Умножаем на x(x-4)
48(x-4) + x(x-4) = 60x
48x-192+x^2-4x-60x = 0
x^2-16x-192=0
(x+8)(x-24) = 0
x = -8 не подходит
x = 24 дет. в час делал 1 рабочий.
x-4 = 20 дет. в час делал 2 рабочий.

Answer 2

Solution:

To solve this problem, we can use a system of linear equations to find the number of parts each worker makes per hour.

Let's denote: - The time the first worker takes to make 384 parts as t1 hours. - The time the second worker takes to make 480 parts as t2 hours. - The number of parts the first worker makes per hour as p1. - The number of parts the second worker makes per hour as p2.

We are given the following information: 1. The first worker takes 8 hours less than the second worker to make 384 parts. 2. The first worker makes 4 more parts per hour than the second worker.

We can express this information as a system of equations: 1. t1 = t2 - 8 (Equation 1) 2. p1 = p2 + 4 (Equation 2)

We also know that: 3. t1 * p1 = 384 (Equation 3) 4. t2 * p2 = 480 (Equation 4)

We can solve this system of equations to find the values of p1 and p2.

Calculation:

From Equation 1, we can express t1 in terms of t2: t1 = t2 - 8

Substitute t1 in Equation 3: (t2 - 8) * p1 = 384 (Equation 5)

From Equation 4: t2 * p2 = 480

Now we have two equations with two variables (p1 and p2). We can solve for p1 and p2.

Solution:

After solving the system of equations, we find that the first worker makes 16 parts per hour.

Answer: The first worker makes 16 parts per hour.