If 9 workers can build a brick wall in 20 days, how many workers will be required to build the exact same wall in 12 days?
Get the complete, step-by-step math solution for: "If 9 workers can build a brick wall in 20 days, how many workers will be required to build the exact same wall in 12 days?". Powered by SolveForX AI math tutor.
Step-by-Step Solution
Step 1: Understand the relationship
This problem involves an inverse proportion. The number of workers (W) and the number of days (D) required to complete a task are inversely proportional. This means that if you increase the number of workers, the number of days required to complete the same work decreases, and vice versa. The total work done remains constant.
Step 2: Identify given values
From the problem statement, we are given the initial number of workers (W1) and the initial number of days (D1). We are also given the new number of days (D2) and need to find the new number of workers (W2).
Step 3: Substitute values into the formula
Now, we substitute the known values into the inverse proportion formula. We have 9 workers initially taking 20 days, and we want to find W2 workers who can complete the work in 12 days.
Step 4: Solve for the unknown
First, we multiply 9 by 20 to get 180. Then, to find W2, we divide 180 by 12. This calculation gives us the required number of workers.