1. **Problem statement:** We have 20 builders working 7 hours a day finishing a building in 30 days. (a) Find how many builders are needed to finish the building in 20 days if they work 10 hours a day. (b) State one assumption made in part (a). 2. **Formula and concept:** Work done is proportional to the number of workers, hours per day, and number of days. Mathematically, total work $W$ can be expressed as: $$W = \text{builders} \times \text{hours/day} \times \text{days}$$ Since the building is the same, $W$ is constant. 3. **Step-by-step solution for (a):** Let $x$ be the number of builders needed. Given: $$20 \times 7 \times 30 = x \times 10 \times 20$$ Calculate the left side: $$20 \times 7 \times 30 = 4200$$ So: $$4200 = 200x$$ Solve for $x$: $$x = \frac{4200}{200} = 21$$ So, 21 builders are needed. 4. **Answer for (b):** We assume that all builders work at the same rate and efficiency, and the work output is directly proportional to the number of builders and hours worked. **Final answers:** (a) 21 builders (b) Assumption: All builders have equal productivity and work output scales linearly with number of builders and hours worked.