3 boys or 5 girls can clean a compound in 8 hours. in how many hours will 2 boy 2 girls clean the same compound
To find out how many hours it would take for 2 boys and 2 girls to clean the compound, we can calculate their combined work rate.
First, let's determine the work rate of each person. We know that 3 boys or 5 girls can clean the compound in 8 hours. Therefore, the work rate of 3 boys is equal to the work rate of 5 girls.
Work rate of 3 boys = Work rate of 5 girls
Let's assume the work rate of a boy is "B" and the work rate of a girl is "G".
Work rate of 3 boys = 3B
Work rate of 5 girls = 5G
According to the given information, their work rates are equal:
3B = 5G
We can simplify this equation by dividing both sides by 3:
B = (5/3)G
Now, let's calculate the work rate of 2 boys and 2 girls working together. Let's assume their work rate is "X".
Work rate of 2 boys + Work rate of 2 girls = X
Using the work rates we calculated earlier:
2B + 2G = X
Substituting B = (5/3)G:
(2(5/3)G) + 2G = X
(10/3)G + 2G = X
(16/3)G = X
So, the work rate of 2 boys and 2 girls together is (16/3) times the work rate of a single girl.
Now, let's find out how many hours it would take for them to clean the compound by using the combined work rate:
Work rate = Amount of work / Time
The amount of work remains the same since they are cleaning the same compound, and we want to find the time it takes for them to complete the work. So, we can write:
(16/3)G = Amount of work / Time
Let's assume it takes T hours for 2 boys and 2 girls to clean the compound.
(16/3)G = Amount of work / T
Since we are comparing the work rate of the girls, we can replace G with 1 (assuming a single girl's work rate is 1):
(16/3)(1) = Amount of work / T
16/3 = Amount of work / T
To find T, we need to calculate the reciprocal of 16/3:
T = 3/16
To simplify this fraction, we can find the decimal value:
T ≈ 0.1875
Therefore, it would take approximately 0.1875 hours (or approximately 11.25 minutes) for 2 boys and 2 girls to clean the same compound.