Question

Игорь и Паша красят забор за 12 часов Паша и Володя красят этот же забор за 15 часов а Володя и Игорь за 20 часов За сколько часов мальчики красят забор работая втроём

Answer 1

1/12+1/20+1/15=(5+3+4)/60=12/60=1/5. 1:1/5=1*5/1=5мин. (за 5минут ребята покраски 1/2 забора,т.к. складывая1//12,1/15 и 1/20 мы количество ребят как бы удвоили , т.е. каждого из ребят прибавили дважды). 5*2=10минут ребятам понадобится для окраски всего забора

Answer 2

To solve this problem, we can use the concept of "work rates." The work rate is a measure of how much work a person or a group of people can complete in a given amount of time. Let's denote the work rate of Igor, Pasha, and Volodya as I, P, and V, respectively.

We know the following information:

1. Igor and Pasha together can paint the fence in 12 hours.
2. Pasha and Volodya together can paint the fence in 15 hours.
3. Volodya and Igor together can paint the fence in 20 hours.

Let's set up three equations based on the work rates:

1. Work rate of Igor and Pasha combined: (I + P) = 1 fence / 12 hours

2. Work rate of Pasha and Volodya combined: (P + V) = 1 fence / 15 hours

3. Work rate of Volodya and Igor combined: (V + I) = 1 fence / 20 hours

Now, we need to find the combined work rate of all three boys working together, denoted as (I + P + V) = 1 fence / x hours.

To find the combined work rate, we can add up the three equations:

(I + P) + (P + V) + (V + I) = (I + P + V)

Substitute the given work rates:

1/12 + 1/15 + 1/20 = (I + P + V)

Now, let's find the common denominator for 12, 15, and 20, which is 60:

(5/60) + (4/60) + (3/60) = (I + P + V)

Now add the fractions:

12/60 = (I + P + V)

Simplify:

1/5 = (I + P + V)

So, the combined work rate of all three boys is 1 fence every 5 hours.

Now, we know their combined work rate. To find out how many hours it takes for them to paint the fence, we need to take the reciprocal:

5 hours / 1 fence = 5 hours

Therefore, the three boys will paint the fence working together in 5 hours.