Question

While covering a distance of $30\mathrm{km}$. Ajeet takes $2$ hours more than Amit. If Ajeet doubles his speed, he would take $1$ hour less than Amit. Find their speeds of walking.

Answer 1

Determine the speeds of their walking.

Let the speed of Ajeet and Amit be $a$ and $b$.

We know that $Time\left(t\right)=\frac{Dis\tan ce\left(d\right)}{Speed\left(S\right)}$

According to the question:

$$\begin{gathered} \frac{30}{a}=2+\frac{30}{b}\cdots \cdots \cdots \cdots \left(1\right) \\ \frac{30}{2a}=\frac{30}{b}-1\cdots \cdots \cdots \cdots \left(2\right) \end{gathered}$$

Subtract equation $\left(2\right)$ from $\left(1\right)$, we get:

$\begin{array}{rcl}\frac{30}{2a}& =& 3\\ & \Rightarrow & a=\frac{30}{6}\\ \therefore a& =& 5\end{array}$

Now, substitute $a=5$ in equation $\left(1\right)$ we get:

$$\begin{gathered} \frac{30}{a}=2+\frac{30}{b} \\ \Rightarrow \frac{30}{5}=2+\frac{30}{b} \\ \Rightarrow 6=2+\frac{30}{b} \\ \Rightarrow b=\frac{30}{4} \\ \therefore b=7.5 \end{gathered}$$

Hence, the required speeds of Ajeet and Amit are $5km/hr$ and $7.5km/hr$.