Final answer:
To find the common labor wage rate per hour in 1913, a proportion between the 2007 and 1913 common labor indexes and their respective wages was used, resulting in an estimated wage rate of approximately $0.19 per hour for 1913.
Step-by-step explanation:
We are given January 2007 data where the ENR 20-city construction common labor index is 16,520.53 with a corresponding wage rate of $31.39 per hour.
We need to find out what the common labor wage rate per hour was in 1913 when the common labor index had a value of 100. To do this, we will use a proportion since we are told that labor rates increased proportionally to the common labor index:
16,520.53 / 31.39 = 100 / x
Where x represents the common labor wage rate per hour in 1913.
Solving for x, we multiply both sides of the equation by x and then divide both sides by 16,520.53 to isolate x on one side:
x * 16,520.53 = 31.39 * 100
x = (31.39 * 100) / 16,520.53
Performing the calculation gives us:
x ≈ $0.19 per hour