Question

There is a regular bus service between towns A and B, with a bus leaving towns A and B every $T$ minutes. A cyclist moving with a speed of $20km{h}^{-1}$ in the direction A to B notices that a bus goes past him every $18$ minutes in the direction of his travel and every $6mins$ in the opposite direction. What is the speed with which buses travel between towns A and B? (Assume the speeds to be constant.)

• A. $30km{h}^{-1}$
• B. $40km{h}^{-1}$
• C. $50km{h}^{-1}$
• D. $60km{h}^{-1}$

Answer 1

Answer: (B)

$40km{h}^{-1}$

Let velocity of bus is $V$. Then separation between two nearest buses is $VT$

A bus moving in same direction travels the distance $VT$ in $18mins$ to meet the cyclist.
So $t=\frac{Srel}{Vrel}\Rightarrow \frac{18}{60}hrs=\frac{VT}{V-20}......\left(1\right)\{Vrel=V-20\}$
A bus moving in opposite direction travels the distance $VT$ in $6mins$ to meet the cyclist.
So $t=\frac{Srel}{Vrel}\Rightarrow \frac{6}{60}=\frac{VT}{V+20}......\left(2\right)\{Vrel=V+20\}$
From $\left(1\right)$ and $\left(2\right)$ we get
$3=\frac{V+20}{V-20}$
$\Rightarrow V=40km/hr$