Question

In a week, Mike ran 8 km farther than Bill, while Pete ran 1 km less than 3 times as far as Bill. If Pete ran 15 km farther than Mike, how many kilometers did Bill run?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{distance}\mathrm{travelled}\mathrm{by}\mathrm{Bill}=x\mathrm{km} \\ \mathrm{Then}\mathrm{the}\mathrm{distance}\mathrm{travelled}\mathrm{by}\mathrm{Mike}=\left(x+8\right)\mathrm{km} \\ \mathrm{Now},\mathrm{distance}\mathrm{travelled}\mathrm{by}\mathrm{Pete}=\left(3x-1\right)\mathrm{km} \\ \mathrm{According}\mathrm{to}\mathrm{question}, \\ \left(3x-1\right)-\left(x+8\right)=15 \\ \Rightarrow 3x-1-x-8=15 \\ \Rightarrow 3x-x=15+1+8 \\ \Rightarrow 2x=24 \\ \Rightarrow x=\frac{24}{2} \\ \Rightarrow x=12 \\ \mathrm{So},\mathrm{distance}\mathrm{travelled}\mathrm{by}\mathrm{Bill}=12\mathrm{km} \end{gathered}$$