BECE Mathematics 2011 Paper

Method ISpeed $=\frac{\text{Distance}}{\text{Time}}$Distance $=$ Speed $\times$ TimeSpeed is the same.$2\;\frac{1}{2}=\frac{2\times2+1}{2}$$2\;\frac{1}{2}=\frac{4+1}{2}$$2\;\frac{1}{2}=\frac{5}{2}$Speed $=60\;\mathrm{km}$ per hourTime $=\frac{5}{2}$Distance $=60\;\mathrm{km}\times\frac{5}{2}$2 divides itself 1 and 60, 30.$\text{Distance}=30\;\mathrm{km}\times5$$\text{Distance}=150\;\mathrm{km}$ Method IIUsing proportionality.60 km per hour means a distance of 60 km is covered in an hour.$\text{If}\;1\;\text{hour}=60\;\mathrm{km}$$\frac{5}{2}\;\text{hour}=60\;\mathrm{km}\times\frac{5}{2}\div1\;\text{hour}$$\frac{5}{2}\;\text{hour}=30\;\mathrm{km}\times5$$\frac{5}{2}\;\text{hour}=150\;\mathrm{km}$ Method IIIThe car covers 60 km an hour $\frac{1}{2}$ an hour the car will cover $\frac{60\;\mathrm{km}}{2}$ $\frac{1}{2}$ an hour the car will cover 30 km $2\;\frac{1}{2}=1$ hour +1 hour $+\frac{1}{2}$ hour Distance covered in $2\;\frac{1}{2}$ hours $=60\;\mathrm{km}+60\;\mathrm{km}+30\;\mathrm{km}$ Distance covered in $2\;\frac{1}{2}$ hours $=150\;\mathrm{km}$