Question

Вася может убрать класс за 42 мин,Петя-за 56 мин.Известно, что если они работают вместе, то производительность их труда понижается на 1/5. За сколько минут совместной работы они уберут класс? Решение в дробях.

Answer 1

1/42 класса уберет Вася за минуту
1/56 класса уберет Петя за минуту
1/42+1/56= 7/168=1/24 класса убрали бы вместе, если бы не снижения
1-1/5=4/5 останется производительности
1/24*4/5=1/30 производительность вместе
1:1/30=30 минут понадобится им вместе

Answer 2

Problem Analysis

We are given that Vasya can clean a classroom in 42 minutes and Petya can clean it in 56 minutes. When they work together, their productivity decreases by 1/5. We need to find out how long it will take for them to clean the classroom together.

Solution

To solve this problem, we can use the concept of work rates. The work rate is defined as the amount of work done per unit of time. Let's assume that Vasya's work rate is v and Petya's work rate is p.

From the given information, we know that Vasya can clean the classroom in 42 minutes, so his work rate is 1/42 of the classroom per minute. Similarly, Petya's work rate is 1/56 of the classroom per minute.

When they work together, their combined work rate is the sum of their individual work rates. However, we are told that their productivity decreases by 1/5 when they work together. This means that their combined work rate is only 4/5 of their individual work rates.

Let's calculate their combined work rate:

Vasya's work rate (v): 1/42 of the classroom per minute

Petya's work rate (p): 1/56 of the classroom per minute

Combined work rate (c): (4/5) * (v + p)

Now, we can find out how long it will take for them to clean the classroom together by using the formula:

Time = Amount of work / Combined work rate

In this case, the amount of work is the entire classroom, which is equal to 1.

Time = 1 / Combined work rate

Let's substitute the values and calculate the time:

Combined work rate (c): (4/5) * (1/42 + 1/56)

Time = 1 / [(4/5) * (1/42 + 1/56)]

Simplifying the expression:

Time = 1 / [(4/5) * (14/294 + 10/294)]

Time = 1 / [(4/5) * (24/294)]

Time = 1 / [(4/5) * (4/49)]

Time = 1 / (16/245)

Time = 245 / 16

Time = 15.3125 minutes

Therefore, it will take Vasya and Petya approximately 15.3125 minutes to clean the classroom together.

Answer

Vasya and Petya will clean the classroom together in approximately 15.3125 minutes.