1. **State the problem:** We know 36 men can slash a field of 160 meters in 10 days. We want to find how long it will take 48 men to slash a field of 128 meters. 2. **Understand the relationship:** The work done is proportional to the number of men and the number of days. More men means less time needed, and the length of the field affects the total work. 3. **Define variables:** Let $T$ be the number of days 48 men take to slash 128 meters. 4. **Work formula:** Work done = Number of men $\times$ Number of days $\times$ Length of field Since the work rate per man per day is constant, we have: $$36 \times 10 \times 160 = 48 \times T \times 128$$ 5. **Solve for $T$:** $$36 \times 10 \times 160 = 48 \times 128 \times T$$ $$57600 = 6144 \times T$$ $$T = \frac{57600}{6144}$$ $$T = 9.375$$ 6. **Interpret the result:** It will take 48 men approximately 9.375 days, or 9 days and 3 hours, to slash the 128-meter field.