Question Number 223125 by BaliramKumar last updated on 15/Jul/25
Answered by mr W last updated on 16/Jul/25
$${A}\:{needs}\:\mathrm{85}{s}\:{for}\:{one}\:{round}, \\ $$$${B}\:{needs}\:\mathrm{45}{s}\:{for}\:{one}\:{round}. \\ $$$${case}\:\mathrm{1}:\:{they}\:{run}\:{in}\:{opposite}\:{directions} \\ $$$${say}\:{they}\:{meet}\:{after}\:{time}\:{t}\:{for}\:{the} \\ $$$${n}^{{th}} \:{time} \\ $$$$\frac{{t}}{\mathrm{85}}+\frac{{t}}{\mathrm{45}}={n} \\ $$$$\Rightarrow{t}=\frac{\mathrm{765}{n}}{\mathrm{26}} \\ $$$${position}\:{of}\:{A}: \\ $$$$\frac{\mathrm{1}}{\mathrm{85}}×\frac{\mathrm{765}{n}}{\mathrm{26}}=\frac{\mathrm{9}{n}}{\mathrm{26}}\:\Rightarrow\mathrm{26}\:{different}\:{points} \\ $$$$\left.\Rightarrow{answer}\:\mathrm{3}\right) \\ $$$$ \\ $$$${case}\:\mathrm{2}:\:{they}\:{run}\:{in}\:{same}\:{direction} \\ $$$$\frac{{t}}{\mathrm{45}}−\frac{{t}}{\mathrm{85}}={n} \\ $$$$\Rightarrow{t}=\frac{\mathrm{765}{n}}{\mathrm{8}} \\ $$$${position}\:{of}\:{A}: \\ $$$$\frac{\mathrm{1}}{\mathrm{85}}×\frac{\mathrm{765}{n}}{\mathrm{8}}=\frac{\mathrm{9}{n}}{\mathrm{8}}\:\Rightarrow\mathrm{8}\:{different}\:{points} \\ $$
Commented by BaliramKumar last updated on 16/Jul/25
$${thanks}\:{sir} \\ $$