Question

Barbarra and catherine started walking to a shopping mall at the same time. barbara walked at 60 metres per minute while cate
herine walked 45 metres per minute. when barabara reached to shopping mall catherine had to go 60 metres more to reach. how far was the shopping mall?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{distance}\mathrm{to}\mathrm{the}\mathrm{shopping}\mathrm{mall}\mathrm{be}\mathrm{x}\mathrm{m}. \\ \mathrm{Now},\mathrm{when}\mathrm{Barabara}\mathrm{reaches}\mathrm{to}\mathrm{the}\mathrm{shopping}\mathrm{mall},\mathrm{Catherine}\mathrm{was}60\mathrm{m}\mathrm{away}\mathrm{from} \\ \mathrm{the}\mathrm{shopping}\mathrm{mall},\mathrm{so}\mathrm{the}\mathrm{distance}\mathrm{covered}\mathrm{by}\mathrm{the}\mathrm{Catherine}\mathrm{at}\mathrm{this}\mathrm{time}=\left(\mathrm{x}-60\right)\mathrm{m}. \\ \mathrm{Time}\mathrm{taken}\mathrm{by}\mathrm{Barabara}\mathrm{to}\mathrm{cover}\mathrm{the}\mathrm{distance}\mathrm{x}\mathrm{m} \\ {\mathrm{t}}_1=\frac{\mathrm{x}}{60}\mathrm{minutes}\left[\mathrm{Time}=\frac{\mathrm{distance}\mathrm{covered}}{\mathrm{speed}}\right] \\ \mathrm{Time}\mathrm{taken}\mathrm{by}\mathrm{Catherine}\mathrm{to}\mathrm{cover}\mathrm{the}\mathrm{distane}\mathrm{of}\left(\mathrm{x}-60\right)\mathrm{m} \\ {\mathrm{t}}_2=\frac{\mathrm{x}-60}{45}\mathrm{minutes}\left[\mathrm{Time}=\frac{\mathrm{distance}\mathrm{covered}}{\mathrm{speed}}\right] \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{the}\mathrm{question}: \\ {\mathrm{t}}_1={\mathrm{t}}_2 \\ \Rightarrow \frac{\mathrm{x}}{60}=\frac{\mathrm{x}-60}{45} \\ \Rightarrow 45\mathrm{x}=60\left(\mathrm{x}-60\right)\left[\mathrm{By}\mathrm{cross}\mathrm{multiplication}\right] \\ \Rightarrow 45\mathrm{x}=60\mathrm{x}-3600 \\ \Rightarrow 15\mathrm{x}=3600 \\ \Rightarrow \mathrm{x}=\frac{3600}{15}=240\mathrm{m}\left[\mathrm{dividing}\mathrm{both}\mathrm{sides}\mathrm{by}15\right] \\ \mathrm{The}\mathrm{distance}\mathrm{to}\mathrm{the}\mathrm{shopping}\mathrm{mall}\mathrm{is}240\mathrm{m}. \end{gathered}$$