# Problems involving time and speed ,

I have a test coming up and there will be a similar question like this . But I don't understand it but I got lucky during a practice .

The question is - A cargo train enters a 1.8km tunnel and takes 80 seconds to emerge . The train takes another 12 seconds to completely leave the tunnel.

(A) what is the speed of the train, in km/h

Total time taken = 80s = 0.0222.. Hrs

Speed = 1.8 / 0.0222.. = 81km/h.

For part a), I'm not sure why do I take 80s ? What's the difference anyway if I add the 12s ?

(B) what is the length of the train in metres ?

Length = 12/3600 X 81 = 270m

For part b) , I'm not sure why I take 12s ?

• You use $1800km$ when stating the problem, but $1.8km$ in your solution. Should that be $1800m$? Mar 10, 2016 at 15:36
• @J.Bush Oh yeah .. It was a typo Mar 10, 2016 at 15:36
• You use 80 seconds to calculate the speed of the train because that is the time it took the front of the train to travel 1800 meters. Now that you know the speed you use the fact that it took 12 seconds for the back of the train to reach where the front of the train was to get the length. Mar 10, 2016 at 15:38

(A)

You start measuring time from when the front of the train enters the tunnel. You stop measuring time when the front of the train leaves the tunnel. The length of the train is irrelevant for this, so you can ignore the time it takes for the back of the train to leave.

The reason that you take $80s$ is because speed is defined as $$speed=\frac{distance}{time}$$ If we measure the distance that the train travels in a certain period of time, we will have the speed of the train. The train travels $1.8km$ in $80s = 0.0\bar2 h$. Therefore the speed of the train can be found to be $$speed = \frac{distance}{time}=\frac{1.8km}{0.0\bar2h}=81\frac{km}{h}$$

(B)

How do we find the length of the train? Well we know $$\text{Difference in time for front of train and back of train to exit tunnel} = 12s = 0.00\bar3h \\ \text{Speed of train} = 81\frac{km}{h}$$ So what can we do with this information? Well we can find the length of the train by the formula $$distance = speed \cdot time\\distance =(81 \frac {km}{h})\cdot 0.00\bar3h \\ distance = 0.27km \\ distance = 270m$$ Which means the length of our train is $270m$. Why are we taking the time $12s$? Because it is the time that the back of the train (travelling at $speed = 81\frac{km}{h}$) to "catch up" to where the front of the train is. We can use this information to find how far the back of the train needs to travel to "catch up" to the front of the train (note that it never catches the front of the train because the front of the train is moving away from it at the same speed that it is chasing at).