1. **State the problem:** 5 men can dig 2 holes in 21 days. We want to find how many more men are needed to dig 6 holes in the same 21 days. 2. **Understand the relationship:** The amount of work done is proportional to the number of men and the number of days. We use the formula: $$\text{Work} = \text{Men} \times \text{Days}$$ 3. **Calculate the work rate for 5 men:** $$\text{Work for 2 holes} = 5 \times 21 = 105 \text{ man-days}$$ This means 105 man-days are needed to dig 2 holes. 4. **Find man-days per hole:** $$\frac{105 \text{ man-days}}{2 \text{ holes}} = 52.5 \text{ man-days per hole}$$ 5. **Calculate total man-days needed for 6 holes:** $$6 \times 52.5 = 315 \text{ man-days}$$ 6. **Find how many men are needed to complete 315 man-days in 21 days:** $$\text{Men} = \frac{315}{21} = 15$$ 7. **Calculate how many more men are needed:** $$15 - 5 = 10$$ **Answer:** 10 more men are needed to dig 6 holes in 21 days at the same rate.