Three people take $2 rac{1}{2}$ hours to deliver leaflets to 270 houses - OCR - GCSE Maths - Question 3 - 2020 - Paper 1

Next, we find out how much time it takes for one person to deliver leaflets to 405 houses. Since 270 houses take $\frac{5}{6}$ hours, we can set up a proportion: $\frac{\frac{5}{6} \text{ hours}}{270 \text{ houses}} = \frac{x}{405 \text{ houses}}$ Cross-multiplying gives: $270x = 405 \times \frac{5}{6}$

Solving for $x$: $x = \frac{405 \times \frac{5}{6}}{270} = \frac{405 \times 5}{1620} = \frac{2025}{1620} = \frac{15}{12} = \frac{5}{4} \text{ hours}$

Since we now know that it takes one person $\frac{5}{4}$ hours for 405 houses, for 5 people, we divide this time by 5: $\text{Time for 5 people} = \frac{5}{4} \div 5 = \frac{5}{4} \times \frac{1}{5} = \frac{1}{4} \text{ hours}$

Finally, converting $\frac{1}{4}$ hours into minutes: $\frac{1}{4} \text{ hours} = 15 \text{ minutes}$