BECE Mathematics 2010 Paper

Concept:More students working means less time is needed, so time and number of students are in inverse proportion.Explanation:Let $t$ be the time in minutes and $s$ be the number of students.Since time is inversely proportional to students, we write $t \propto \frac{1}{s}$.Introduce a constant $k$: $t = \frac{k}{s}$.Given that 6 students take 1 hour, convert 1 hour to 60 minutes: $60 = \frac{k}{6}$.Thus, $k = 60 \times 6 = 360$.So the relation is $t = \frac{360}{s}$.For 15 students: $t = \frac{360}{15} = 24$ minutes.Answer:15 students will take 24 minutes to sweep the compound.Correct option: A. 24 minutes.