Ten people can paint 60 houses in 120 days, so five people can paint 30 houses in:
everything is halved so 120/2= 60 days
The sixty houses take (10 men)(120 days) = 1200 man-days to complete. Then one house would take (1200 man-days) / (60 houses) = 20 man-days / house.
How many man-days are required for thirty houses?
If those man-days are divided amongst five people, how many days must each person spend?
To find out how long five people can paint 30 houses, we can use the concept of man-days, which represents the number of days it would take for one person to complete one house.
Given that ten people can paint 60 houses in 120 days, we can calculate the number of man-days required to paint one house:
10 people x 120 days = 1200 man-days
From this, we can determine that it takes 1200 man-days to paint 60 houses, which means it takes 20 man-days to paint one house:
1200 man-days ÷ 60 houses = 20 man-days per house
Now, we can calculate the number of man-days required to paint 30 houses:
20 man-days per house x 30 houses = 600 man-days
Since we want to know how many days it would take for five people to complete the job, we divide the total number of man-days by the number of people:
600 man-days ÷ 5 people = 120 days
Therefore, five people can paint 30 houses in 120 days.
To find the number of days it would take for five people to paint 30 houses, we need to use the concept of proportions.
Let's set up the proportion based on the information given:
(10 people / 60 houses) = (5 people / 30 houses)
To solve this proportion, we can cross-multiply:
(10 * 30) = (60 * 5)
300 = 300
Since both sides of the equation are equal, we can conclude that the proportion is true.
Now, we need to determine the number of days for five people to paint 30 houses. Since we know that 10 people can paint 60 houses in 120 days, we can set it up as another proportion:
(10 people / 120 days) = (5 people / x days)
Cross-multiplying:
(10 * x) = (120 * 5)
10x = 600
Dividing both sides by 10:
x = 60
Therefore, five people can paint 30 houses in 60 days.