The time needed to paint a wall varies directly with the area and inversely with the number of painters.If it takes 5 people 2 hours to paint 100 square meters,how much area could 6 people paint in one hour.
t = ka/p
So, pt/a = k is constant.
So, you want a such that
6*1/a = 5*2/100
To solve this problem, we can use the variation formula:
t = k * (A / p)
where:
t = time needed to paint the wall (in hours)
k = constant of variation
A = area of the wall (in square meters)
p = number of painters
Given that it takes 5 people 2 hours to paint 100 square meters, we can plug these values into the variation formula:
2 = k * (100 / 5)
Simplifying this equation, we get:
2 = k * 20
Now, we can solve for the constant of variation, k:
k = 2 / 20
k = 1/10
So, the constant of variation is 1/10.
Now, we need to find how much area can be painted in one hour with 6 people. Let's use the variation formula again:
t = k * (A / p)
Now, substitute the known values into the formula:
1 = (1/10) * (A / 6)
To find A, cross multiply and solve for A:
6 = 1/10 * A
Multiply both sides by 10:
60 = A
Therefore, 6 people can paint 60 square meters in one hour.