Two cities $X$ and $Y$ are connected by a regular bus service with a bus leaving in either direction

Question

Two cities $X$ and $Y$ are connected by a regular bus service with a bus leaving in either direction every $T$ min . A girl is driving scooty with a speed of $60 \mathrm{~km} / \mathrm{h}$ in the direction $X$ to $Y$ notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period $T$ of the bus service and the speed (assumed constant) of the buses.

Professor PC Thomas Classes · Answer

(b) : The relative velocity of the bus in the same direction of motion of scooty $=V_B-V_S=V_B-60$ The relative velocity of the bus in the opposite direction of motion of scooty $=V_B+V_S=V_B+60$ Now, distance travelled by bus in time $(T)=V_B T$ Now, setting up equations for the distances between the buses in both cases and solve for $T$ and $V_B$. $\begin{aligned} & \frac{V_B T}{V_B-60}=30 \ & \frac{V_B T}{V_B+60}=10\end{aligned}$ \ By solving equations (i) and (ii), we get
$
T=15 \mathrm{~min} 	ext { and } V_B=120 \mathrm{~km} / \mathrm{h}
$