Question

A train, 400 m long crosses an electric pole in 12 sec. Find the speed of the train in km/hr?

Answer 1

Hint: We start solving the problem by recalling the fact that train should move 400 m in order to completely cross the given electric pole. We recall the definition of speed as the ratio of distance to time to find the speed in m/s. We then use the results $1m=\dfrac{1}{1000}km$, $1s=\dfrac{1}{3600}hr$ and make necessary calculations to find the speed of train in km/hr.

Complete step-by-step answer:
According to the problem, we are given that a 400 m train crosses an electric pole in 12 sec. We need to find the speed of the train in km/hr.
We know that while a train crosses the pole, the starting point of the train crosses pole first and the ending point of pole crosses last. In order to cross the lost train should move 400 m forward at a certain speed. Let us assume that speed be v.
We know that speed is defined as the ratio of distance to time. So, \[\text{speed}=\dfrac{\text{distance}}{\text{time}}\].
Now, we need to find the speed of the train which travelled 400 m in 12 secs.
So, the speed of the train $\left( v \right)$ = $\dfrac{400}{12}=\dfrac{100}{3}m/s$.
We know that $1km=1000m\Leftrightarrow 1m=\dfrac{1}{1000}km$ and $1hr=3600s\Leftrightarrow 1s=\dfrac{1}{3600}hr$.
$\Rightarrow $ Speed of the train $\left( v \right)$ = $\dfrac{100}{3}\times \dfrac{\dfrac{1}{1000}}{\dfrac{1}{3600}}km/hr$.
$\Rightarrow $ Speed of the train $\left( v \right)$ = $\dfrac{100}{3}\times \dfrac{3600}{1000}km/hr$.
$\Rightarrow $ Speed of the train $\left( v \right)$ = $120km/hr$.
So, we have found the speed of the train as 120 km/hr.
∴ The speed of the train is 120 km/hr.

Note: We should know that the train crosses the electric pole if and only if the total length of the train is crossed which is the main point we use in finding the speed of the train. We should not stop solving the problem after finding the speed of the train in m/s as we need to find speed in km/hr. We can also find the speed in km/min by using the fact that $1\min =\dfrac{1}{60}hr$. Similarly, we can expect problems to find the time taken by train to travel between two stations at a distance of 60km.