Question

Задача 1/2. Ученик, работая самостоятельно, может поштукатурить всю стену площадью 10 м² за то время, за которое мастер может поштукатурить две таких стены. Мастер и ученик, работая вместе, могут поштукатурить всю стену за 6 ч. За какое время ученик может поштукатурить всю стену, работая самостоятельно?​

Answer 1

Пошаговое объяснение:

1) 10 * 2 = 20 (м²) - штукатурит мастер за то время, за которое ученик штукатурит 10м²

2)

х - время за которое ученик поштукатурит всю стену ученик работая самостоятельно

10/х + 20/х = 10/6

30/х = 10/6

х = 30 : 10/6

х = 30 * 6/10

х = 180/10

х = 18

За 18 часов поштукатурит всю стену ученик

Answer 2

10:2=5

5*6=30

1+2=3

30:2=15

15+3=18

Answer 3

Problem Analysis

We are given that a student can plaster an entire wall with an area of 10 m² in the same amount of time that a master can plaster two such walls. When the master and the student work together, they can plaster the entire wall in 6 hours. We need to determine how long it would take for the student to plaster the entire wall working alone.

Solution

Let's assume that the time it takes for the student to plaster the entire wall alone is x hours.

From the given information, we know that: - The student can plaster an entire wall with an area of 10 m² in x hours. - The master can plaster two such walls in the same amount of time. - When the master and the student work together, they can plaster the entire wall in 6 hours.

To solve this problem, we can set up the following equation based on the work rates of the student and the master:

Student's work rate: 1 wall / x hours

Master's work rate: 2 walls / x hours

Combined work rate: 1 wall / 6 hours

Since the combined work rate is the sum of the individual work rates, we can write the equation:

1/x + 2/x = 1/6

To solve for x, we can multiply both sides of the equation by 6x to eliminate the denominators:

6 + 12 = x

x = 18

Therefore, the student can plaster the entire wall working alone in 18 hours.

Answer

The student can plaster the entire wall, with an area of 10 m², working alone in 18 hours.