Question

(xii) Points A and B are 70 km apart on a highway. A car starts from A and another car starts from B at the same time. If they travel in the same direction, they meet in 7 hours, but if they travel towards each other they meet in one hour. What are their speeds?

Answer 1

Let the speed of car that starts from point A be v_A km/h
and the speed of car that starts from point B is v_B km/h
$$\begin{gathered} \mathrm{According}\mathrm{to}\mathrm{the}\mathrm{question}, \\ \left(v_A-v_B\right)\times 7=70 \\ \Rightarrow 7v_A-7v_B=70...\left(1\right) \\ \left(v_A+v_B\right)\times 1=70 \\ \Rightarrow v_A+v_B=70 \\ {v}_A=70-v_B....\left(2\right) \\ \mathrm{Substituting}\mathrm{eq}\left(2\right)\mathrm{in}\mathrm{eq}\left(1\right)\mathrm{we}\mathrm{get}, \\ 7\left(70-v_{\mathrm{B}}\right)-7v_{\mathrm{B}}=70 \\ \Rightarrow 490-7v_{\mathrm{B}}-7v_{\mathit{B}}=70 \\ \Rightarrow 14v_{\mathrm{B}}=420 \\ \Rightarrow v_{\mathrm{B}}=30\mathrm{km}/\mathrm{h} \\ {v}_{\mathrm{A}}=\left(70-30\right)\mathrm{km}/\mathrm{h}=40\mathrm{km}/\mathrm{h} \\ \mathrm{Hence},\mathrm{the}\mathrm{speed}\mathrm{of}\mathrm{the}\mathrm{car}\mathrm{that}\mathrm{starts}\mathrm{from}\mathrm{the}\mathrm{point}\mathrm{A}\mathrm{is}40\mathrm{km}/\mathrm{h} \\ \&\mathrm{speed}\mathrm{of}\mathrm{the}\mathrm{car}\mathrm{that}\mathrm{starts}\mathrm{from}\mathrm{point}\mathrm{B}\mathrm{is}30\mathrm{km}/\mathrm{h} \end{gathered}$$