Question

The distance between two stations is 300 km. Two motorcyclists start simultaneously from these stations and move towards each other. The speed of one of them is 7 km/h more than that of the other. If the distance between them after 2 hours of their start is 34 km, find the speed of each motorcyclist. Check your solution.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{speed}\mathrm{of}\text{one}\mathrm{motorcyclist}\mathrm{be}x\mathrm{km}/\mathrm{h}. \\ \text{So,}\mathrm{the}\mathrm{speed}\mathrm{of}\text{the}\mathrm{other}\mathrm{motorcyclist}\mathrm{will}\mathrm{be}(x+7)\mathrm{km}/\mathrm{h}. \\ \text{D}\mathrm{istance}\mathrm{travelled}\mathrm{by}\text{the}\mathrm{first}\mathrm{motorcyclist}\mathrm{in}2\mathrm{hours}=2x\mathrm{km} \\ \text{D}\mathrm{istance}\mathrm{travelled}\mathrm{by}\text{the}\mathrm{second}\mathrm{motorcyclist}\mathrm{in}2\mathrm{hours}=2(\mathit{}x+7)\mathrm{km} \\ \text{Therefore,} \\ 300-(2x+(2x+14))=34 \\ \Rightarrow 300-(2x+2x+14)=34 \\ \Rightarrow 300-4x-14=34 \\ \Rightarrow 286-4x=34 \\ \Rightarrow 286-34=4x \\ \Rightarrow 252=4x \\ \Rightarrow x=\frac{252}{4}=63 \\ \mathrm{Therefore},\mathrm{the}\mathrm{speed}\mathrm{of}\mathrm{the}\mathrm{first}\mathrm{motorcyclist}\mathrm{is}63\mathrm{km}/\mathrm{h}. \\ \mathrm{The}\mathrm{speed}\mathrm{of}\mathrm{the}\mathrm{second}\mathrm{motorcyclist}\mathrm{is}(\mathrm{x}+7)=(63+7)=70\mathrm{km}/\mathrm{h}. \\ \mathbf{Check}\mathbf{:} \\ \mathrm{The}\mathrm{distance}\mathrm{covered}\mathrm{by}\mathrm{the}\mathrm{first}\mathrm{motorcyclist}\mathrm{in}2\mathrm{hours}=63\times 2=126\mathrm{km} \\ \mathrm{The}\mathrm{distance}\mathrm{covered}\mathrm{by}\mathrm{the}\mathrm{second}\mathrm{motorcyclist}\mathrm{in}2\mathrm{hours}=70\times 2=140\mathrm{km} \\ \mathrm{The}\mathrm{distance}\mathrm{between}\mathrm{the}\mathrm{motorcyclists}\mathrm{after}2\mathrm{hours}=300-(126+140)=34\mathrm{km}(\mathrm{which}\mathrm{is}\mathrm{the}\mathrm{same}\mathrm{as}\mathrm{given}) \\ \mathrm{Therefore},\mathrm{the}\mathrm{speeds}\mathrm{of}\mathrm{the}\mathrm{motorcyclists}\mathrm{are}63\mathrm{km}/\mathrm{h}\mathrm{and}70\mathrm{km}/\mathrm{h},\mathrm{respectively}. \end{gathered}$$