Redhill Secondary School has hired a team of 8 workers to repaint its basketball and netball courts. If the number of workers is decreased by 2 , the entire job will take 3 more days to complete. Assuming that all the workers work at the same rate, how many more workers should be hired so that the job can be completed 3 days earlier? Let the no. of days to finish when 8 w

Let \( D \) be the number of days it takes for 8 workers to complete the job. The total amount of work can be expressed in terms of worker-days, which is the product of the number of workers and the number of days they work. Therefore, the total work \( W \) can be expressed as: \[ W = 8D \] If the number of workers is decreased by 2 (to 6 workers), the job will take 3 more days to complete, so the new number of days is \( D + 3 \). The total work can also be expressed as: \[ W = 6(D + 3) \] Since both expressions represent the same total work \( W \), we can set them equal to each other: \[ 8D = 6(D + 3) \] Expanding the right side: \[ 8D = 6D + 18 \] Now, subtract \( 6D \) from both sides: \[ 2D = 18 \] Dividing both sides by 2 gives: \[ D = 9 \] So, it takes 8 workers 9 days to complete the job. The total work is: \[ W = 8D = 8 \times 9 = 72 \text{ worker-days} \] Now, we want to find out how many more workers should be hired so that the job can be completed 3 days earlier. If the job is to be completed 3 days earlier, it will take: \[ D - 3 = 9 - 3 = 6 \text{ days} \] Let \( x \) be the number of workers needed to complete the job in 6 days. The total work can also be expressed as: \[ W = x \times 6 \] Setting this equal to the total work we calculated earlier: \[ x \times 6 = 72 \] Solving for \( x \): \[ x = \frac{72}{6} = 12 \] Since we originally had 8 workers, the number of additional workers needed is: \[ 12 - 8 = 4 \] Thus, **4 more workers should be hired** to complete the job 3 days earlier.