Question

Коля может вскопать грядку за 45 минут, а папа - за 36 минут. Известно, что если они работают вместе, то производительность их труда повышается на 1/9. За сколько минут совместной работы они вскопают грядку?

Answer 1

У коли производительность на грядку будет 45*8/9=40 минут, а у папы 36*8/9=32 минуты.
Теперь найдем общую суммарную производительность.
1/40+1/32=(4+5)/160=9/160 - это такую часть грядки коля с папой вскапывают за 1 минуту.
Соответственно на всю грядку они вдвоем затратят 160/9=17 7/9 минут

Answer 2

Problem Analysis

We are given that Kolya can dig a bed in 45 minutes and his father can dig the same bed in 36 minutes. When they work together, their productivity increases by 1/9. We need to determine how many minutes it will take for them to dig the bed together.

Solution

Let's assume that the total work required to dig the bed is 1 unit.

We can calculate the individual work rates of Kolya and his father using the given information. Kolya can dig the bed in 45 minutes, so his work rate is 1/45 units per minute. Similarly, his father's work rate is 1/36 units per minute.

When they work together, their combined work rate is the sum of their individual work rates. Let's denote the combined work rate as R.

R = Kolya's work rate + Father's work rate

R = 1/45 + 1/36

To find the time it takes for them to dig the bed together, we can use the formula:

Time = 1 / R

Let's calculate the value of R and then find the time.

Calculation

R = 1/45 + 1/36

R = (4/180) + (5/180)

R = 9/180

Time = 1 / R

Time = 180 / 9

Time = 20 minutes

Answer

Kolya and his father will dig the bed together in 20 minutes.

Explanation

When Kolya and his father work together, their combined work rate is 9/180 units per minute. This means that they can dig 9/180 of the bed in one minute. To dig the entire bed, which is 1 unit of work, they will need 180/9 minutes, which simplifies to 20 minutes.