Question

If two buses are moving in the opposite directions, their speed having $35\text{ km/hr}$ and $30\text{ km/hr}$ respectively, find their relative speed?
A. $5\text{ km/hr}$
B. $15\text{ km/hr}$
C. $25\text{ km/hr}$
D. $65\text{ km/hr}$

Answer 1

As we have given the individual speeds of the buses moving in the opposite directions. We assume the speeds to be $u$ and $v$. We calculate the relative speed by adding their individual speeds and choose the option which matches our answer.

Complete step-by-step answer :
We have given the speed of two buses moving in the opposite directions, their speed having $35\text{ km/hr}$ and $30\text{ km/hr}$ respectively.
We have to find their relative speed.
Let us assume the speed of the first bus is $u=35\text{ km/hr}$.
Speed of second bus is $v=30\text{ km/hr}$
Speed is known as the distance traveled per unit time. We can describe the relative speed as the speed of the body moving with respect to other. When two bodies are moving in the opposite direction, relative speed is calculated by adding their speeds.
Now, buses are moving in the opposite direction, so the relative speed will be $\left( u+v \right)\text{ km/hr}$
We get
$\begin{aligned} & \text{Relative speed = }35+30\text{ km/hr} \\\ & \text{Relative speed = 65 km/hr} \\\ \end{aligned}$
So, the relative speed of buses moving in the opposite direction is $\text{65 km/hr}$.
Option D is the correct answer.

Note : The possibility of mistake is that one can take the relative speed to be the difference, which gives the wrong answer. If the buses instead of moving in opposite directions were moving in the same direction, we would have subtracted the individual speeds of buses to obtain the relative speed of buses.