Question

2. Розв'яжи задачу. За 5 год учень столяра виготовив стільки деталей, скільки майс тер — за 3 год. Скільки деталей зробив учень, якщо разом за одну годину вони виготовляють 32 деталей Даю 15 балов

Answer 1

Ответ:

Пошаговое объяснение:

Пусть ученик изготовил Х деталей

Мастер Y

X + Y = 32 детали/ час

Ученик за 5 часов изготовил 5 Х деталей

Мастер за 3 часа изготовил 3 Y деталей

5 Х = 3 Y

X = 32-Y

5 Х = 3 Y

5 ( 32- Y) = 3 Y

160 -5Y = 3Y

160 = 8 Y,

Y = 160/8

Y = 20 деталей - мастер

X = 32-Y = 32-20 = 12 деталей - ученик.

Проверяем за 3 часа мастер сделает 60 деталей, учение за 5 часов также 60 деталей.

Answer 2

Task Solution

To solve this problem, we can use the concept of proportionality. Let's denote the number of details made by the apprentice in 5 hours as A, and the number of details made by the master in 3 hours as B. We are given that together they make 32 details in 1 hour.

Using the concept of proportionality, we can set up the following equation:

Apprentice's rate: A details / 5 hours = A/5 details per hour Master's rate: B details / 3 hours = B/3 details per hour

Given that together they make 32 details in 1 hour, we can express their combined rate as:

A/5 + B/3 = 32 details per hour

Now, we can solve for A and B to find the number of details made by the apprentice and the master.

Calculation

To solve for A and B, we can use the equation A/5 + B/3 = 32 and solve for A.

Multiplying the equation by 15 (the least common multiple of 5 and 3) to clear the denominators, we get:

3A + 5B = 480

Now, we need another equation to solve for A and B. We know that the apprentice made A details in 5 hours and the master made B details in 3 hours. Since they make the same number of details in 1 hour, we can express this as:

A/5 = B/3

Cross-multiplying, we get:

3A = 5B

Now, we have a system of equations: 3A + 5B = 480 3A = 5B

Solving this system of equations will give us the values of A and B, which represent the number of details made by the apprentice and the master, respectively.

Solution

Solving the system of equations, we find: A = 200 B = 120

So, the apprentice made 200 details, and the master made 120 details.

Therefore, the apprentice made 200 details in 5 hours.