Final answer:
In this problem, the number of hours required to complete a job is inversely proportional to the number of workers available. Using the given information, we can set up a proportion and solve for the number of additional workers needed to complete the job 60 hours earlier.
Step-by-step explanation:
This question involves a situation where the number of hours required to complete a job is inversely proportional to the number of workers available. Inverse proportionality means that as one variable increases, the other variable decreases.
We can set up a proportion to solve this problem. Let h represent the number of hours and n represent the number of workers. From the given information, we know that when there are 7500 workers, it takes 75 hours to complete the job.
Using the proportion h/n = k, where k is a constant of proportionality, we can solve for k:
75/7500 = k
k = 1/100
Now we can use the value of k to find the number of workers needed to complete the job 60 hours earlier. Let w represent the additional number of workers needed:
75/(7500 + w) = (75 - 60)/(7500)
Simplifying this equation, we get:
(75 - 60)/(7500) = 75/(7500 + w)
Cross-multiplying, we have:
15(7500 + w) = 75(7500)
Expanding the equation:
112500 + 15w = 562500
Subtracting 112500 from both sides:
15w = 450000
Dividing both sides by 15:
w = 30000
Therefore, 30000 more workers are needed to complete the job 60 hours earlier.