To determine how many days it will take for 10 workers to complete the same task if 5 workers can complete it in 10 days, we can use the concept of work rate.

First, let’s find the work rate of the workers.

If 5 workers can complete the task in 10 days, then the total amount of work can be expressed as: $Total Work=5 workers\times 10 days=50 worker-days\backslash text\{Total\; Work\}\; =\; 5\; \backslash text\{\; workers\}\; \backslash times\; 10\; \backslash text\{\; days\}\; =\; 50\; \backslash text\{\; worker-days\}$Total Work=5 workers×10 days=50 worker-days

This means that 50 worker-days are required to complete the task.

Next, we want to find out how long it will take for 10 workers to complete the same amount of work. Let $DD$D be the number of days it takes for 10 workers to complete the task.

We know: $10 workers\times D days=50 worker-days10\; \backslash text\{\; workers\}\; \backslash times\; D\; \backslash text\{\; days\}\; =\; 50\; \backslash text\{\; worker-days\}$10 workers×D days=50 worker-days

Solving for $DD$D: $D=\frac{50 worker-days}{10 workers}=5 daysD\; =\; \backslash frac\{50\; \backslash text\{\; worker-days\}\}\{10\; \backslash text\{\; workers\}\}\; =\; 5\; \backslash text\{\; days\}$D=10 workers50 worker-days​=5 days

So, it will take 10 workers 5 days to complete the task, assuming they work at the same rate.