Time, Speed and Distance: Problems on Trains

Problems on trains are very common in competitive exams. Various types of questions are asked on trains. Questions on trains are solved using the concept of time, speed and distance i.e. we use the formulas of time, speed and distance to solve questions on trains.
Given below is a list of some important points that need to be kept in mind while solving questions on trains.
Important Points
  • When two trains are going in the same direction, then their relative speed is the difference between the two speeds.
  • When two trains are moving in the opposite direction, then their relative speed is the sum of the two speeds.
  • When a train crosses a stationary man/ pole/ lamp post/ sign post- in all these cases, the object which the train crosses is stationary and the distance travelled is the length of the train.
  • When it crosses a platform/ bridge- in these cases, the object which the train crosses is stationary and the distance travelled is the length of the train and the length of the object.
  • When two trains are moving in same direction, then their speed will be subtracted.
  • When two trains are moving in opposite directions, then their speed will be added.
  • In both the above cases, the total distance is the sum of the length of both the trains.
  • When a train crosses a car/ bicycle/ a mobile man- in these cases, the relative speed between the train and the object is taken depending upon the direction of the movement of the other object relative to the train- and the distance travelled is the length of the train.
Now, let us try doing some questions and understand the concept of solving train related problems
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Solved Questions
Question 1: A train travelling at 60 kmph crosses a man in 6 seconds. What is the length of the train?
Solution: Speed in m/sec = 60 *(5/18) = 50/3 m/sec
Time taken to cross the man = 6 secs
Therefore, Distance = (50/3)* 6 = 100 metres (i.e. the length of the train)
Question 2: A train travelling at 60 kmph crosses another train travelling in the same direction at 50 kmph in 30 seconds. What is the combined length of both the trains?
Solution: Speed of train A = 60 kmph = 60* (5/18) = 50/3 m/sec
Speed of train B = = 50 kmph = 50 *(5/18) = 125/9 m/sec
The relative speed =(50/3)-(125/9)=25/9 m/s (we have subtracted the two values because both the trains are going in the same direction)
Time taken by train A to cross train B = 30 secs
Distance = Speed * Time
Distance =25/9 * 30 = 250/3 metres (i.e. the combined length of both trains)
Question 3: Train A, 600 mts long is running at 80 kmph will take how much time to cross a man sitting in another train which is 400 mtres long, running at 64 kmph in the opposite direction?
Solution: Distance = 600 metres
Total Speed = 64 + 80 = 144 kmph (added because they are travelling in opposite directions)
In m/sec, speed = 144 *(5/18) = 40 m/sec
Distance = Speed * Time
600 = 40 * Time
Therefore, Time = 15 seconds
Question 4: Two trains start at the same time from Pune and Delhi and proceed towards each other at 80 kmph and 95 kmph respectively. When they meet, it is found that one train has travelled 180 km more than the other. Find the distance between Delhi and Pune.
Solution: Let t be the time after they meet
Distance1 = Speed * Time = 80 * t = 80t
Distance2 = Speed * Time = 95 * t = 95t
As the distance gap between both trains is 180 kms
Therefore, we can say that:
95t - 80t = 180
15t = 180
t = 12 seconds
Total Distance, (95+80) t = 175 * 12 (t = 12)
Distance = 2100 kms
Question 5: The distance between two places A and B is 570 kms. A train starts from A at 50 kmph at 6 am and another starts from B at 80 kmph at 7 am towards each other. At what time will they meet?
Solution: Let the two trains meet at a distance x km from place A
Time required by the train starting from A to cover x is x/50 hr
Time taken by the other train starting from B to cover (570 - x) km = (570-x)/80
But the first train has started 1 hr early. So, it has travelled 50 km in this 1 hr.
Therefore, x/50 - 1= (570-x)/80
On Solving, x = 250
So, they will meet at a distance of 250 km from place A
So the time at which they will meet will be (250/50) = 5 hrs (after 6 am)
Hence, they will meet at 11 am.
Question 6: The average speed of a train without stoppages is 48 kmph and average speed with stoppages is 40 kmph. How many minutes in an hour the train stops on an average?
Solution: If the train were to travel without stoppages, it would cover 48 km.
With stoppages, the average speed reduces by (48-40) = 8 km
Therefore, (8/48)* 60 minutes = 10 minutes
Hence, 10 minutes would be the time per hour the train stops on an average.
Question 7: Indrayani Express leaves Pune for Bombay at 17:30 hrs and reaches Bombay at 21:30 hrs. While, Shatabdi, which leaves Bombay at 17:00 hrs reaches Pune at 20:30 hrs. At what time do they pass each other?
Solution: Let the distance between Bombay and Pune = d km
Indrayani’s Speed =(d/4) kmph and that of Shatabdi = (d/3.5)kmph
Let t be the time in hrs after Shatabdi has left for Pune, when the two trains meet
Therefore, distance travelled by Shatabdi = (d/3.5)* t
And that of Indrayani =(d/4) * (t-30/60)
The sum of the distances travelled by the two trains = distance between Bombay and Pune = d km
Therefore, (d/3.5)* t +(d/4) * (t-30/60)=d
Solving for t, we get t = 2.1 hrs or 2 hrs and 6 mins
Hence, the two trains meet at 19:06 hrs
Question 8: How long will a 150 m long train running at a speed of 60 kmph take to cross a bridge of 300 m?
Solution: Total Distance = 300 + 150 = 450 m
Speed = 60 kmph = 60 *(5/18)=(50/3) m/sec
Distance = Speed * Time
450 =(50/3) * Time
Time = 27 seconds
 
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