1. **Problem statement:** Paul and Andrew tiled a hall of area 325 square feet. Paul worked first alone, then Andrew finished the job alone. The total time was 4.5 hours. We need to find how many square feet Andrew laid. 2. **Given data:** - Total area $A = 325$ sq ft - Paul's rate: 15 sq ft per 20 minutes = $\frac{15}{20} = 0.75$ sq ft per minute - Andrew's rate: 20 sq ft per 15 minutes = $\frac{20}{15} = \frac{4}{3} \approx 1.333$ sq ft per minute - Total time $T = 4.5$ hours = 270 minutes 3. **Define variables:** - Let $t_p$ = time Paul worked (minutes) - Let $t_a$ = time Andrew worked (minutes) 4. **Formulate equations:** - Total time: $t_p + t_a = 270$ - Total area tiled: $0.75 t_p + \frac{4}{3} t_a = 325$ 5. **Solve the system:** From total time: $t_p = 270 - t_a$ Substitute into area equation: $$0.75(270 - t_a) + \frac{4}{3} t_a = 325$$ $$202.5 - 0.75 t_a + \frac{4}{3} t_a = 325$$ Combine like terms: $$-0.75 t_a + 1.333 t_a = 325 - 202.5$$ $$0.583 t_a = 122.5$$ $$t_a = \frac{122.5}{0.583} \approx 210$$ minutes 6. **Calculate area Andrew laid:** $$\text{Area}_a = \frac{4}{3} \times 210 = 280$$ sq ft **Final answer:** Andrew laid 280 square feet of tiles.