Question

An auto-rickshaw takes $3$ hours to cover a distance of $36km$. If its speed is increased by $4km/h$, the time taken by it to cover the same distance is __________.

Answer 1

Step 1: Given data.

An auto-rickshaw takes $3$ hours to cover a distance of $36km$.

Speed is increased by $4km/h$.

Step 2: Formula to be used.

The time $T$ can be calculated by $T=\frac{D}{S}$, when distance $D$ and speed $S$ is given.

The speed $S$ can be calculated by $S=\frac{D}{T}$, when distance $D$ and time $T$ is given.

Step 3: Find the time taken by the auto-rickshaw after increasing the speed.

In the question, it is given that an auto-rickshaw takes $3$ hours to cover a distance of $36km$.

So, the speed $S_1$ of the Auto-rickshaw is given by:

$$\begin{gathered} S_1=\frac{36}{3} \\ \Rightarrow S_1=12km/h \end{gathered}$$

So, before increasing the speed the speed of the auto-rickshaw is $12km/h$.

In the question, it is given that the speed is increased by $4km/h$.

So, the speed of auto-rickshaw after increasing the speed is given by: $S_2=16km/h$.

Assume that, the time taken by the auto-rickshaw to cover the same distance after increasing the speed is $t$.

So, the time taken by the auto-rickshaw to cover the same distance after increasing the speed is given by:

$$\begin{gathered} t=\frac{36}{S_2} \\ \Rightarrow t=\frac{36}{16} \\ \Rightarrow t=2.25hrs \end{gathered}$$

Which is $2hrs15min$

Therefore, the time taken by auto-rickshaw to cover the same distance is $2hrs15min$.