Lesson Other basic arithmetic Travel & Distance problems

Other basic arithmetic Travel & Distance problems

Problem 1

The speed of 36 kilometers per hour is the same as   = 10 meters per second.


Since the train passes a telegraph post in 12 seconds, it means that in 12 seconds 
the train covers the distance equal to its length. The distance is

    time*rate = 12 seconds * 10 meters per second = 120 meters.


Hence, the length of the train is 120 meters.


ANSWER.  The length of the train is 120 meters.

Problem 2

So, every 12 seconds the train moves 96 meters forward.  So, its speed is  

    {{96/8}}} = 12 meters per second,  or   = 43. kilometers per hour.


ANSWER.  The speed of the train is 43.2 kilometers per hour.

Problem 3

The speed of 36 kilometers per hour is the same as   = 10 meters per second.


From the moment the front of the train comes up to the closest end of the platform to the moment 
the rear of the train comes up to the other end, the train moves forward 90 + 120 = 210 meters.


Hence, the time for the train to pass the platform is   = 21 seconds.


ANSWER.  The time for the train to pass the platform is   = 21 seconds.

Problem 4

The speed of 54 kilometers per hour is the same as   = 15 meters per second.


From the moment the front of the train comes up to the closest end of the tunnel to the moment 
the rear of the train comes up to the other end, the train moves forward 120 + 180 = 300 meters.


Hence, the time for the train to pass the tunnel is   = 20 seconds.


ANSWER.  The time for the train to pass the tunnel is   = 20 seconds.

Problem 5

For passing the bridge, the train should move forward 1440 meters plus its own length. The train spends 65 seconds for it

For passing the tunnel, the train should move forward 1680 meters plus its own length. The train spends 75 seconds for it

So, the train spends 75-65 = 10 seconds to cover the distance equal the difference 1680-1440 = 240 meters.


From it, we find the speed of the train as   = 24 meters per second, or  = 86.4 kilometers per hour.

          
Next, in 65 seconds, the train moves forward in 65*24 = 1560 meters.

Of them, 1560 - 1440 = 120 meters is the length of the train.


Thus the train length is 120 meters and the train speed is 24 meters per second, or 86.4 kilometers per hour.

Problem 6

The starting moment for our consideration is when the trains noses 
touch the same plane perpendicular to the tracks.


At this time moment, the ending points of the trains are at the distance
equal to the sum of the lengths of trains, i.e.  

     =  =   of a mile.


These two ending points moves/approach toward each other with the speed, 
which is the sum of the speeds of the trains, i.e. 40 + 50 = 90 miles per hour. 
It is the relative speed approaching the ending points.


The process will complete when the ending points will meet each other.


The time is the initial distance between end points divided by the relative speed of approaching

     =  =  of an hour,

which is 13 seconds.