BECE Mathematics 2010 Paper

The more the students, the lesser the time.Hence time $(t)$ is inversely proportional to the number of students (s).$t \propto \; \frac{1}{s}$Remove the proportionality by introducing a constant $(k)$.$t = k \times \; \frac{1}{s}$Use the known information to solve for $k$6 students used 1 hour.1 hour $=60$ minutes.60 minutes $=k \times \; \frac{1}{6}$$\;k = 6 \times 60$$\;k = 360$The general equation is:$\;t = 360 \times \; \frac{1}{s}$$\;t = \; \frac{360}{s}$ Calculate how long it will take 15 students to sweep.$\; s = 15$$\;t = \; \frac{360}{15}$Note:1. The hours was converted to minutes hence time obtained would be in minutes2. 15 divides itself 1 and $360, 24$ times$t = 24 \; \text{ minutes } \;$It will take 15 students 24 minutes to sweep the compound.