The number of volunteers V, needed to pick apples from an apple tree orchid varies directly with the number of apple trees A, and inversely with the time T they have for picking. If we know from experience that 20 volunteers can pick apples from 100 apple trees in 2.5 hours, find the constant of variation and use it to find out how many volunteers is needed for 180 apple trees orchid that needs 2 hours picking. Show work
We can start by using the formula for direct and inverse variation:
V = k(A/T)
where k is the constant of variation.
We are given that 20 volunteers can pick 100 apple trees in 2.5 hours. We can use this information to solve for k:
20 = k(100/2.5)
20 = k(40)
k = 20/40
k = 0.5
So the constant of variation is 0.5.
To find out how many volunteers are needed for 180 apple trees orchid that needs 2 hours picking, we can use the same formula:
V = k(A/T)
V = 0.5(180/2)
V = 45
Therefore, 45 volunteers are needed for the 180 apple trees orchid that needs 2 hours picking.
To find the constant of variation, we can use the given information.
We know that the number of volunteers V varies directly with the number of apple trees A, and inversely with the time T.
From the given data:
V = 20, A = 100, and T = 2.5
We can set up the equation using the form of variation:
V = k * (A / T)
Substituting the given values, we have:
20 = k * (100 / 2.5)
Simplifying:
20 = k * 40
Dividing both sides by 40:
k = 0.5
Now that we have the constant of variation (k = 0.5), we can use it to find the number of volunteers needed for 180 apple trees that need 2 hours of picking.
Using the variation equation:
V = k * (A / T)
Substituting the given values:
V = 0.5 * (180 / 2)
Simplifying:
V = 0.5 * 90
V = 45
Therefore, 45 volunteers are needed for the 180 apple trees orchard that needs 2 hours of picking.