Question Number 42145 by Tawa1 last updated on 18/Aug/18
Commented by MrW3 last updated on 18/Aug/18
$${it}\:{moves}\:\mathrm{2}\:{meters}\:{in}\:\mathrm{8}\:{seconds}.\:{for} \\ $$$${the}\:{first}\:\mathrm{6}\:{meters}\:{it}\:{needs}\:\mathrm{24}\:{seconds}. \\ $$$${then}\:{it}\:{moves}\:\mathrm{5}\:{steps}\:{and}\:{falls}\:{into}\:{the} \\ $$$${pit}.\:{i}.{e}.\:{it}\:{falls}\:{into}\:{the}\:{pit}\:{after}\:\mathrm{29}\:{s}. \\ $$
Commented by Tawa1 last updated on 18/Aug/18
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$
Answered by Necxx last updated on 18/Aug/18
$${distance}\:{covered}\:{in}\:\mathrm{1}\:{step}=\mathrm{1}{m} \\ $$$${timetaken}=\mathrm{1}{s} \\ $$$${timetaken}\:{to}\:{move}\:{first}\:\mathrm{5}{m}\:{forward} \\ $$$$=\mathrm{5}{s} \\ $$$${timetaken}\:{to}\:{move}\:\mathrm{3}{m}\:{backwards} \\ $$$$=\mathrm{3}{s} \\ $$$${hence},{the}\:{net}\:{distance}\:{travelled}=\mathrm{5}−\mathrm{3} \\ $$$$=\mathrm{2}{m} \\ $$$${net}\:{timetaken}\:{to}\:{cover}\:{this}\:\mathrm{2}{m}=\mathrm{8}{s} \\ $$$$ \\ $$$${if}\:{the}\:{drunkard}\:{covers}\:\mathrm{2}{m}\:{in}\:\mathrm{8}{s},{then} \\ $$$${distance}\:{covered}\:{in}\:\mathrm{8}{m}=\frac{\mathrm{8}×\mathrm{8}}{\mathrm{2}}=\mathrm{32}{s} \\ $$$${since}\:{there}\:{is}\:{still}\:{a}\:{remainder}\:{of} \\ $$$$\mathrm{5}{m}\:{which}\:{can}\:{be}\:{covered}\:{in}\:\mathrm{5}{s} \\ $$$$ \\ $$$${then}\:{the}\:{total}\:{time}\:{taken}\:{for}\:{the} \\ $$$${drunkard}\:{to}\:{enter}\:{a}\:{pit}\:\mathrm{13}{m}\:{away} \\ $$$$=\mathrm{32}+\mathrm{5}=\mathrm{37}{s} \\ $$
Commented by MrW3 last updated on 19/Aug/18
$${the}\:{pit}\:{is}\:\mathrm{11}\:{m}\:{away},\:{not}\:\mathrm{13}\:{m}! \\ $$
Commented by Necxx last updated on 20/Aug/18
$${oh}….{I}\:{didnt}\:{take}\:{note}\:{of}\:{that}.{Thanks} \\ $$