Question

A train travels a distance of $540km$ in $9$ hours. How much will this train take to travel $330km$ ?

Answer 1

Hint: To find the time taken by the train to travel $330km$, let us assume the time taken by the train to travel $330km$ is $t$ hours. It is given that the distance travelled by the train crosses $=540km$ and the time taken to travel this distance $=9$ hours . We will be using the formula, $\text{Speed}=\text{ }\dfrac{\text{Distance}}{\text{Time}}$ . We will substitute the values of each case, that is, distances in this equation. Since the speed of the train is constant, let us equate these two equations, that is, \[\dfrac{540}{9}=\dfrac{330}{t}\] . Solving this gives the value of $t$ .

Complete step by step answer:
We need to find the time taken by the train to travel $330km$ .
We know that $\text{Speed}=\text{ }\dfrac{\text{Distance}}{\text{Time}}$
It is given that the distance travelled by the train crosses $=540km$
Also, the time taken to travel $540km$ $=9$ hours .
Let us substitute these in the formula for speed. Thus,
$\Rightarrow \text{Speed}=\text{ }\dfrac{540}{9}...(i)$
Let us assume that the time taken by the train to travel $330km$ is $t$ hours.
So, the speed for this will be given by,
$\Rightarrow \text{Speed}=\text{ }\dfrac{330}{t}...(ii)$
The speed of the train is constant. Hence, we can equate the equations $(i)$ and $(ii)$ .
Hence, we get
\[\Rightarrow \dfrac{540}{9}=\dfrac{330}{t}\]
Let us solve the equation to get the value of $t$ .
$\Rightarrow 540t=330\times 9$
Let us do the multiplication operation. We will get
$\Rightarrow 540t=2970$
From this, we will get
$\Rightarrow t=\text{ }\dfrac{2970}{540}=5.5$

Hence, the time taken by the train to travel $330km$ is $5.5$ hours or $\text{5 hours 30 minutes}$.

Note: The question specifies the time in hours so the time for $330km$ should also be in hours. There can be a chance to make error in speed formula like $\text{Speed}=\text{ }\dfrac{\text{Time}}{\text{Distance}}$ that leads the entire solution to be wrong. An easier way to remember the speed formula is by remembering its unit $m/s$ .