A contractor needs 2 men and 5 litres of paint to paint a fence wall,40m * 3m in 9hours. How many men and how much paint does he need to paint a fence wall 20m *12m in 3 hours. The men all work at same rate.
since the work needed is proportional to the area to be painted, he will need (20*12)/(40*3) = 2 times as much paint, or 10 liters.
If it takes the same time, he will need 2 times as many men, or 4 men.
But, since he wants it done in 1/3 the time, he will need 3 times as many men, or 12 men.
Well, let's do some math and apply a touch of humor here.
If a contractor needs 2 men and 5 liters of paint to paint a fence wall that is 40m * 3m in 9 hours, we first need to figure out their speed of painting. So, with some serious calculations and abracadabra, let's say each man paints at a rate of 40 meters per hour. Now, let's move on to the paint situation. This fence wall seems to have an affinity for paint!
So, if the contractor needs to paint a fence wall that is 20m * 12m in just 3 hours, we'll have to consider the proportions. Since the area of this wall is half of the previous wall, we can assume the contractor will need half the amount of paint. Therefore, in order to successfully complete the task, the contractor will need 1 man and 2.5 liters of paint.
Remember, these calculations are not an exact science, but it's a funny way to approach the situation. Ultimately, it's always best to consult with a professional or the contractor themselves to determine the exact requirements.
To find out how many men and how much paint the contractor needs, we can use the concept of work rate.
Let's assume that each man's work rate is constant and the same for both scenarios.
Given:
- First scenario: Fence wall dimension = 40m x 3m, time = 9 hours, and 2 men were used with 5 liters of paint.
- Second scenario: Fence wall dimension = 20m x 12m, time = 3 hours.
To calculate the work rate, we can use the formula:
Work Rate = Work / Time
Since the work rate is constant for each man in both scenarios, we can equate the two work rates:
(2 men) * (First Work Rate) = (X men) * (Second Work Rate)
Now, let's find the work rates in each scenario:
First Scenario:
Work Rate = (Fence area) / (Time taken)
= (40m * 3m) / (9 hours)
= (120 m²) / (9 hours)
= 40/3 m²/h
Second Scenario:
Work Rate = (Fence area) / (Time taken)
= (20m * 12m) / (3 hours)
= (240 m²) / (3 hours)
= 80 m²/h
So, by equating the two work rates:
(2 men) * (40/3 m²/h) = (X men) * (80 m²/h)
Now, let's solve for X (the number of men needed):
(2 men) * (40/3 m²/h) = (X men) * (80 m²/h)
Simplifying the equation:
(80/3) = (X/2)
Cross-multiplying:
2 * (80/3) = X
X = (160/3) men
Therefore, the contractor would need approximately 53.33 men (rounded up to the nearest whole number) to paint a fence wall that is 20m x 12m in 3 hours.
Now, let's calculate the amount of paint needed for the second scenario:
The amount of paint required is directly proportional to the fence area. So, we can calculate the ratio of the fence area in the second scenario to the fence area in the first scenario and then multiply it with the amount of paint used in the first scenario.
Paint needed = (Area of second fence / Area of first fence) * Amount of paint used in the first scenario
= (240 m² / 120 m²) * 5 liters
= 2 * 5 liters
= 10 liters
Therefore, the contractor would need 10 liters of paint to paint a fence wall that is 20m x 12m in 3 hours.
To find out how many men and how much paint the contractor needs to paint a 20m * 12m fence wall in 3 hours, we can use proportions based on the given information.
Let's start by establishing a relationship between the amount of work done and the time it takes to complete that work.
In the first scenario, we know it took 2 men 9 hours to paint a fence wall with an area of 40m * 3m. Thus, the total work done can be represented as 2 men x 9 hours = 18 man-hours.
Using the same logic, we can calculate the total work done for the second scenario:
Total work = Number of men x Time
Since we want to find out the number of men and the amount of paint needed, we'll assign variables to represent these unknown quantities. Let's say we have "x" men and "y" liters of paint for the second scenario.
We know that the total work done for the second scenario is equal to the total work done for the first scenario. So, we can set up the following proportion:
2 men x 9 hours = x men x 3 hours
This proportion says that the amount of work done is the same for both scenarios. Now, let's solve for "x":
2 men x 9 hours = x men x 3 hours
18 man-hours = 3x men-hours
18/3 = x
x = 6
Therefore, the contractor needs 6 men to paint the 20m * 12m fence wall in 3 hours.
Next, let's tackle the amount of paint needed.
In the first scenario, we know that 2 men needed 5 liters of paint to complete the job. Since we have already determined that the number of men for the second scenario is 6, we can set up the following proportion:
2 men : 5 liters = 6 men : y liters
To solve for "y", we can cross-multiply and then divide:
2 x y = 6 x 5
2y = 30
y = 15
Therefore, the contractor needs 15 liters of paint to paint the 20m * 12m fence wall in 3 hours with 6 men.
In summary, to paint the fence wall with an area of 20m * 12m in 3 hours, the contractor will need 6 men and 15 liters of paint.