Question

The length of the train is 210m.it passes through a station of length 340m, At a speed of 180km/h. Calculate the number of seconds the train takes to pass completely through the station.

Answer 1

Hint:
Here we need to find the time taken by the train to pass the station. To solve this question, we need to add the length of the train and the station to find the total distance. Then we will divide the total distance by the speed to find the time taken by the train. Here, we will also convert the unit of speed in order to have the same unit for all quantities.
Formula used: Here we will be using the formula \[{\text{time = }}\dfrac{{{\text{distance}}}}{{{\text{speed}}}}\] to solve the question.

Complete step by step solution:
Given the length of the train is 210 m. Here m represents metres.
The given length of the station is 340m.
Now to calculate the total distance we have to add the length of the train and the length of the station.
\[{\text{total distance}} = 210{\text{m}} + 340{\text{m}} = 550{\text{m}}\]
Now the given speed is given in \[{\text{km}}/{\text{hr}}\]. We have to convert it into \[{\text{m}}/{\text{s}}\] in order to have the same unit throughout.
We know that kilometers can be converted to meters using the conversion \[1{\text{km}} = 1000{\text{m}}\].
Now we can convert hour into seconds using the following conversion:
\[1{\text{ hour}} = 60{\text{minutes}}\]…..\[\left[ 1 \right]\]
\[1{\text{ minute}} = 60{\text{seconds}}\]………\[\left[ 2 \right]\]
By multiplying \[\left[ 1 \right]\] and \[\left[ 2 \right]\] we will
\[1{\text{ hour}} = 60 \times 60{\text{seconds}} = 3600{\text{ seconds}}\]
Now, we will convert \[{\text{km}}/{\text{hr}}\] into \[{\text{m}}/{\text{s}}\].
\[1{\text{ km}}/{\text{hr}} = \dfrac{{1000}}{{3600}}{\text{m}}/{\text{s}} = \dfrac{{10}}{{36}}{\text{m}}/{\text{s}}\]
We will now convert the given speed into \[{\text{m}}/{\text{s}}\].
\[\begin{array}{l}{\text{speed}} = 180{\text{km}}/{\text{hr}}\\ = 180 \times \dfrac{{10}}{{36}}{\text{m}}/{\text{s}}\\ = 50{\text{m}}/{\text{s}}\end{array}\]
Now we will substitute \[{\text{distance}} = 550{\text{m}}\] and \[{\text{speed}} = 50{\text{m}}/{\text{s}}\] in the formula \[{\text{time = }}\dfrac{{{\text{distance}}}}{{{\text{speed}}}}\].
\[{\text{time}} = \dfrac{{550{\text{m}}}}{{55{\text{m}}/{\text{s}}}} = 11{\text{s}}\]

\[\therefore\] The time taken by the train to pass the station completely is 11s.

Note:
Here, we need to be careful with the units, while solving the question. We need to remember that we can perform a mathematical operation on two or more numbers only if they have the same unit. If we do that then the answer will be wrong. If two numbers have different units then we have to convert either of them to the same unit as the other number. In this question, we were given speed in \[{\text{km}}/{\text{hr}}\] and distance in metre. In order to solve the question correctly, we changed the unit of speed. We could have also changed the unit of the distance from metre to kilometer by dividing the number by 1000. It is very important for us to have knowledge of the conversion of units.