Final answer:
To find out how many more days it will take to finish the project if the work continues at the same rate, set up a proportion using the amount of work remaining and the time taken to complete (7)/(10) of the work. Solve the proportion to find the number of days.
Step-by-step explanation:
To calculate the remaining time to finish the project, we can use the concept of the production rate. The project manager has determined that (3)/(10) of the work was completed in 9 days. This means that (3)/(10) of the work was completed in 9 days, so (7)/(10) of the work remains. Since the work is progressing at the same rate, we can set up a proportion using the amount of work remaining and the time taken to complete (7)/(10) of the work.
Let x be the number of days it will take to finish the project. The proportion can be written as: (7)/(10) : 9 = 1 : x. Cross-multiplying gives us: (7)/(10) * x = 9 * 1. Simplifying the equation, we get: (7)/(10) * x = 9. To solve for x, we can multiply both sides of the equation by (10)/(7): x = (9 * (10)/(7)). Evaluating the expression, we find that x is approximately 12.86, which means it will take approximately 12.86 more days to finish the project at the same rate of progress.