Final answer:
The constant of variation in this problem is 2.5.
Step-by-step explanation:
To find the constant of variation in this problem, we need to use the formula y = kx, where y represents the number of pieces produced and x represents the number of workers.
In this case, we have y = 40 and x = 16. Plugging these values into the formula, we get 40 = 16k. To solve for k, divide both sides of the equation by 16, so k = 40/16 = 2.5.
Therefore, the constant of variation is 2.5.