Question Number 47810 by Necxx last updated on 15/Nov/18
$${A}\:{mobike}\:{rider}\:{moving}\:{from}\:{A}\:{to}\:{B} \\ $$$${with}\:{speed}\:\mathrm{20}{km}/{h}\:{notices}\:{that}\:{a} \\ $$$${bus}\:{goes}\:{past}\:{it}\:{every}\:\mathrm{21}\:{minute}\:{in} \\ $$$${the}\:{direction}\:{of}\:{his}\:{motion}\:{and} \\ $$$${every}\:\mathrm{7}\:{minutes}\:{in}\:{the}\:{opposite} \\ $$$${direction}.{Velocity}\:{of}\:{the}\:{bus}\:{is} \\ $$$$\left.{a}\left.\right)\left.\mathrm{25}{km}/{h}\:{b}\right)\mathrm{35}{km}/{h}\:{c}\right)\mathrm{30}{km}/{h} \\ $$$$\left.{d}\right)\mathrm{40}{km}/{h} \\ $$$$ \\ $$
Commented by Necxx last updated on 15/Nov/18
$${please}\:{help} \\ $$
Answered by mr W last updated on 15/Nov/18
$${x}={velocity}\:{of}\:{bus}\:{in}\:{km}/{h} \\ $$$$\left({x}+\mathrm{20}\right)×\mathrm{7}/\mathrm{60}=\left({x}−\mathrm{20}\right)×\mathrm{21}/\mathrm{60}={distance}\:{between}\:{two}\:{buses}\:{in}\:{km} \\ $$$$\left({x}+\mathrm{20}\right)×\mathrm{7}=\left({x}−\mathrm{20}\right)×\mathrm{21} \\ $$$${x}=\mathrm{40} \\ $$$$\left.\Rightarrow{answer}\:{d}\right) \\ $$$$ \\ $$$${distance}\:{between}\:{two}\:{buses}\:{is} \\ $$$$\left(\mathrm{40}+\mathrm{20}\right)×\mathrm{7}/\mathrm{60}=\mathrm{7}\:{km} \\ $$$$ \\ $$$$\mathrm{7}/\mathrm{40}×\mathrm{60}=\mathrm{13}\Rightarrow{the}\:{bus}\:{comes}\:{every} \\ $$$$\mathrm{13}\:{minutes} \\ $$
Commented by Necxx last updated on 15/Nov/18
$${Thank}\:{you}\:{so}\:{much}\:{sir} \\ $$