BECE Mathematics 2016 Paper

The more the workers, the lesser time it takes to complete the workTherefore number of workers is inversely proportional to time.Let $w=$ number of workers and $t=$ time$w \propto \frac{1}{t}$Remove the proportionality by introducing equal to and a constantLet $k=$ contant$w= k \times \frac{1}{t}$$w= \frac{k}{t}$Since we know the number of workers and time taken, we can calculate for the value of $k$$w=15$$t=12$$15= \frac{k}{12}$Multiply both sides by 12 to get rid of the denominator.$15 \times 12 = k$The general equation is therefore $w= \frac{15 \times 12}{t}$Now we are given the number of workers to find time.Number of workers $(w)=9$$9= \frac{15 \times 12}{t}$Multiply both sides by $t$ to get rid of the denominator$9 \times t = 15 \times 12$Solve for the value of $t$ by dividing both sides by 9$t= \frac{15 \times 12}{9}$$t=5 \times 4 = 20$Note: 3 divides 12, 4 times and 9, 3 times. 3 divides itself once and 15, 5 times Time taken for the 9 boys is 20 hours.