Question & Answer
QUESTION

A train 210m long took 12 seconds to pass a 90m long tunnel. Find the speed of the train.

ANSWER Verified Verified
Hint: To solve such question we will use the relation of speed, distance and time, the formula of which is given by, \[\text{speed}=\dfrac{\text{distance}}{\text{time}}\]. Using this we will try to determine the required speed of the train.

Complete step-by-step answer:

Given that the train is 210m long and it took 12 seconds to pass a 90m long tunnel.
We have to find the speed of the train. To find the speed of the train, we have to used the formula of speed, that is, \[\text{speed}=\dfrac{\text{distance}}{\text{time}}\],

Given, Length of the train = 210m
Length of the tunnel = 90m
Therefore, the total distance covered by the train = 210 + 90 = 300 m.
Time taken by the train to cover the total distance = 12s.
Now calculating the speed we have,
\[\Rightarrow \]\[\text{speed}=\dfrac{\text{distance}}{\text{time}}\]
\[\begin{align}
  & \Rightarrow \text{speed}=\dfrac{300}{12} \\
 & \Rightarrow \text{speed}=20m/s \\
\end{align}\]

Obtained speed is in meter/second, we have to convert it into kilometers per hour.
We have 1 km = 1000m
Implies 1hr = 3600s
To convert speed from meter/second to kilometer per hour, we have to multiply the speed with \[\dfrac{3600}{1000}\],
Doing so we get,
\[\Rightarrow speed=(25)\left( \dfrac{3600}{1000} \right)\]km/hr
\[\Rightarrow speed=90km/hr\]

Therefore, the speed of the train is 90km/hr.

Note: The possibility of error in this question is that you can do whole calculations without converting the speed from meter per second to kilometer per hour, this won’t be wrong but right speed comes with standard units.