If 10 workers can complete a job in 10 days, how many days would it take 15 workers? Assume indirect proportion.

Step 1: Identify the given values and the type of proportion. This is an inverse proportion problem because as the number of workers increases, the number of days required to complete the job decreases. Given: Initial workers ($W_1$) = 10 workers Initial days ($D_1$) = 10 days New workers ($W_2$) = 15 workers New days ($D_2$) = ?

Step 2: Set up the inverse proportion equation. For inverse proportion, the product of the number of workers and the number of days is constant. $W_1 \times D_1 = W_2 \times D_2$

Step 3: Substitute the known values into the equation. $10 workers \times 10 days = 15 workers \times D_2$

Step 4: Solve for $D_2$. $100 = 15 \times D_2$ $D_2 = \frac{100}{15}$ $D_2 = \frac{20}{3}$ $D_2 = 6\frac{2}{3} \text{ days}$

It would take 15 workers \boxed{6\frac{2{3} days}} to complete the job.

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