Question

A train is moving at a speed of x km/hr. What distance will it cover in 15 hours if it stops for 1 hour at 2 stations?

Answer 1

Hint: We are given that a train is moving at a speed of x km/hr. It moves for 15 hours. We will first use the formula of speed i.e. $\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}$ to find the formula for distance. We will get it as given below:
\[\text{Distance}\left( \text{D} \right)=\text{Speed}\times \text{Time}\]
Given that, we have 15 hours for the total journey out of which 2 hours are used for stoppage. So, we will find the total time for the actual movement. Once, we have the actual time, then we can use the distance formula i.e. $\text{Distance}=\text{Speed}\times \text{Time}$ to find the distance.

Complete step-by-step solution
We are given that a train is moving at a speed of x km/hr. We are asked to find the distance if this train moves for 15 hours. It is also given that the train stops for 1 hour at 2 stations.
Firstly we are given the speed as x km/hr. We know that the speed of any vehicle gives us the ratio of the distance covered by the vehicle to the time taken to cover that distance.
We also know that the formula for speed is given as:
\[\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}\]
If we define distance as D and time as t, we get:
\[\text{Speed}=\dfrac{\text{D}}{\text{t}}\]
In our question, we are asked to find the distance travelled. So, our formula i.e. $\text{Speed}=\dfrac{\text{D}}{\text{t}}$ will get transformed and we get formula for distance as \[\text{D}=\text{Speed}\times \text{Time}\Rightarrow \text{D}=\text{Speed}\times t\]
Now, we are given that train moves for 15 hours. So, ‘t’ must be 15.
As we know that the train stopped at two stations for 1 hour. So the total number of hours the train was stopped was 1+1. So, for 2 hours the train was standing at 2 different stations. So, out of 15 hours of journey, 2 hours were not used as the train was standing. So,
\[\text{Total hour of motion}=\text{15}-\text{2}=\text{13 hours}\]
So, our time on the journey will be 13 hours.
So, t = 13, and speed is given as x km/hr.
Now, using the above-given formula for distance, we get:
Distance traveled by train $\Rightarrow 13\times x=13x$

Note: To find the distance, we have to use that time which is used while the train was moving. We were given 15 hours for the journey but these 15 hours is not totally contributing to the movement of the train, only 13 hours is being used, that’s why we took ‘t’ as 13. Remember, when we multiply a variable with a constant, that variable sticks at the end of the constant. It means $\Rightarrow 13\times x=13x$