Trains, Boats and Streams

Question 1

If two trains are moving in same direction with speeds a km / hr and b km / hr, then their relative speed would be ?

Answer 1

|a – b| km / hr.

Question 2

If two trains are moving in different directions, i.e., coming towards each other or going away from each other, with speeds a km / hr and b km / hr, then their relative speed would be ?

Answer 2

(a + b) km / hr.

Question 3

What would be the Time taken by a train, ‘t’ meters long, to pass a stationary object of length ‘l’ meters

Answer 3

It would be the time taken by the train to travel ‘t + l’ meters. For example, to cover a platform of 800 m, a train of length 200 m moving at the speed of 10 m / s would be the time taken by the train to cover 800 + 200 = 1000 m at the speed of 10 m / s, i.e., 1000 / 10 = 100 s.

Question 4

What would be the time taken by the train to pass a pole or a man or a post (or any stationary object with negligible length as compared to the length of the train, like if the train is 500 m long and a pole is 1 m in length),

Answer 4

the time taken by the train would be the time it takes to travel the length of the train. For example, if a train of length 100 m is moving at the speed of 10 m / s, it would take 100 / 10 = 10 s to pass a pole / man / post.

Question 5

If two trains of lengths L1 and L2 are moving in the same direction with speeds S1 and S2, then the time required by faster train to overtake the slower train would be ?

Answer 5

the time taken to cover an equivalent distance of L1 + L2, with relative speed |S1 – S2|, i.e., Time = (L1 + L2) / |S1 – S2|.

Question 6

If two trains of lengths L1 and L2 are moving in opposite directions with speeds S1 and S2, then the time required by the trains to cross each other completely would be ?

Answer 6

the time taken to cover an equivalent distance of L1 + L2, with relative speed (S1 + S2), i.e., Time = (L1 + L2) / (S1 + S2).

Question 7

If two trains started moving towards each other at the same time with speeds S1 and S2 respectively and after meeting, they take ‘T1’ and ‘T2’ seconds respectively, then what would be the ratio of their speeds with the time taken ?

Answer 7

S1 : S2 = T2^1/2 : T1^1/2

Question 8

What is said to be downstream ?

Answer 8

If the boat is moving in the direction of the stream, it is said to be going downstream

Question 9

When it is said to be upstream ?

Answer 9

if the boat is moving opposite to the direction of stream, it is said to be going upstream.

Question 10

If the speed of boat in still water is B km / hr and speed of the stream is S km / hr,
Speed Upstream = ?
Speed Downstream = ?

Answer 10

Speed Upstream = B – S km / hr

Speed Downstream = B + S km / hr

Question 11

If the speed upstream is U km / hr and speed downstream is D km / hr,
Speed of boat in still water = ?
Speed of stream = ?

Answer 11

Speed of boat in still water = 0.5 x (D + U) km / hr

Speed of stream = 0.5 x (D – U) km / hr

Question 12

Question 1 : A 100 m long train moving at a speed of 60 km / hr passes a man standing on a pavement near a railway track. Find the time taken by the train to pass the man.

Answer 12

Solution : Length of the train = 100 m = 0.1 km
Speed of the train = 60 km / hr
So, time taken by the train to pass the man = time taken to cover 0.1 km at the speed of 60 km / hr
Therefore, time taken by the train to pass the man = 0.1 / 60 hour = (0.1 / 60) x 3600 sec = 6 sec

Question 13

Question 2 : How long does a train 1000 m long moving at a speed of 90 km / hr would take to pass through a 500 m long bridge?

Answer 13

Solution : Here, time taken by the train to pass the bridge completely would be the time it takes to cover 1000 + 500 = 1500 m at the speed of 90 km / hr = 90 x (5/18) = 25 m / sec.
Therefore, time required = 1500 / 25 = 60 sec = 1 minute

Question 14

Question 3 : A man standing near a railway track observes that a train passes him in 80 seconds but to pass by a 180 m long bridge, the same train takes 200 seconds. Find the speed of the train.

Answer 14

Solution : Let the length of the train be L meters.
=> The train covers L meters in 80 seconds and L + 180 meters in 200 seconds, with the same speed.
We know that Speed = Distance / Time.
=> Speed = L / 80 = (L + 180) / 200
=> L / 80 = (L + 180) / 200
=> 2.5 L = L + 180
=> 1.5 L = 180
=> L = 120
Thus, speed of the train = 120 / 80 = 1.5 m / sec

Question 15

Question 4 : Two trains 140 m and 160 m long are moving towards each other on parallel tracks with speeds 40 km / hr and 50 km / hr respectively. How much time would they take to pass each other completely ?

Answer 15

Solution : Total distance to be covered = 140 + 160 m = 300 m
Relative speed = 40 + 50 = 90 km / hr = 90 x (5 / 18) m / sec = 25 m / sec
Therefore, time taken to pass each other = 300 / 25 = 12 sec

Question 16

Question 5 : Two trains 140 m and 160 m long are moving in the same direction on parallel tracks with speeds 40 km / hr and 50 km / hr respectively. How much time would the faster train require to overtake the slower train ?

Answer 16

Solution : Total distance to be covered = 140 + 160 m = 300 m
Relative speed = 50 – 40 = 10 km / hr = 10 x (5 / 18) m / sec = 50 / 18 m / sec
Therefore, time taken by faster train to overtake the slower train = 300 / (50/18) = 108 sec

Question 17

Question 6 : A 500 m long train takes 36 seconds to cross a man walking in the opposite direction at the speed of 10 km / hr. Find the speed of the train.

Answer 17

Solution : Let the speed of the train be T km / hr. 
=> Relative speed = T + 10 km / hr 
=> Length of the train = 500 m = 0.5 km 
We know that Distance = Speed x Time 
=> 0.5 = (T + 10) x (36 / 3600) 
=> 50 = T + 10 
=> T = 40 km / hr 
Therefore, speed of the train is 40 km / hr.

Question 18

Question 7 : A non – stop train started from Delhi towards Mumbai and at the same time, another non – stop train started from Mumbai towards Delhi. If after meeting in Bhopal they took 9 and 16 hours respectively to reach their destinations, find the speed of the train that started from Delhi, given that the speed of the train that started from Mumbai was moving at a speed of 90 km / hr.

Answer 18

Solution : We know that for two trains starting at the same time, S1 : S2 = T21/2 : T11/2
Here, S2 = 90 km / hr
T1 = 9 hrs
T2 = 16 hrs
=> S1 : 90 = 4 : 3
=> S1 = 120 km / hr
Therefore, speed of train that started from Delhi = 120 km / hr

Question 19

Question 8 : A boatman can row a boat upstream at 14 km / hr and downstream at 20 km / hr. Find the speed of the boat in still water and speed of the stream.

Answer 19

Solution : We are given that speed downstream, D = 20 km / hr and speed upstream, U = 14 km / hr
Therefore, Speed of boat in still water = 0.5 x (D + U) km / hr = 0.5 x (14 + 20) = 17 km / hr
Also, speed of the stream = 0.5 x (D – U) km / hr = 0.5 x (20 – 14) = 3 km / hr

Another method :
Speed of the stream = 0.5 x (D – U) = 0.5 x 6 = 3 km / hr
Speed of the boat in still water = Speed of the stream + Speed Upstream = 3 + 14 = 17 km / hr

Question 20

Question 9 : A boatman can row a boat at the speed of 5 km upstream and 15 km downstream. To cover upstream he needs 2.5 hours and to cover downstream, he needs 1.5 hours. Find the speed of the stream and speed of the boat in still water.

Answer 20

Solution : We are given that the boatman covers 5 km upstream in 2.5 hours and 15 km downstream in 10 hours.
=> Speed upstream, U = 5 / 2.5 = 2 km / hr
=> Speed downstream, D = 15 / 1.5 = 10 km / hr
Therefore, Speed of boat in still water = 0.5 x (D + U) km / hr = 0.5 x (10 + 2) = 6 km / hr
Also, speed of the stream = 0.5 x (D – U) km / hr = 0.5 x (10 – 2) = 4 km / hr