Question

Two cars are moving in the same direction at the same speed of $30\mathrm{Km}/\mathrm{Hr}$. They are separated by $5\mathrm{Km}$. What is the speed of a car moving in the opposite direction if it meets the two cars at an interval of $4$ minutes.

Answer 1

Step 1: Given data

Speed, $\mathrm{v}=30\frac{\text{Km}}{\text{Hr}}$

Time, $\mathrm{t}=4\min =\frac{4}{60}\mathrm{hr}$

Distance, $\mathrm{d}=5\mathrm{Km}$

Step 2: Calculate the speed of the third car.

Let's assume the speed of the third car is $u$.

Relative velocity,

$u-v=\frac{d}{t}$

Here,

$u$ is the speed of the third car.

$v$ is the speed of the first car.

$d$ is the distance between them.

$t$ is time.

Relative Velocity.

$$\begin{gathered} \mathrm{u}-\left(-30\frac{\text{Km}}{\text{Hr}}\right)=\frac{5\text{Km}}{4\text{Hr}}\times 60 \\ \mathrm{u}+30=75 \\ \mathrm{u}=45\frac{\text{Km}}{\text{Hr}} \end{gathered}$$

Hence, the speed of the third car is $45\frac{\text{km}}{\text{hr}}$.