Km Per Hour to Meter Per Second, Trains, Total Time and Average Speed in Boats Streams with Solved Examples Video

This is the second lecture of time speed and distance module. In this first I have told about the conversion between km per hour to meter per second. This conversion is very important as it has application in wide variety of questions. I have told that in order to convert x km per hour in meter per second your have to multiply x by 5/18 and vice versa, when we have to convert x meter per second in km per hour then we have to multiply x by 18/5. Why this is the way of interconverting them is explained by me in this video with proper proof and I have also shown its application through a solved question. After that I have taken up the concept of trains. In this, I have explained the concept of effective length when two trains are crossing each other or when a train is crossing a platform or when the train is passing a particular person.After that I have explained the theory of Boats and Stream. The concept of relative speed in boats and streams I have already covered in the previous lecture and in this lecture I have proved the formula of average speed and total time taken in boats and streams.

The average speed in this comes out to be

(Downstream Speed x Upstream Speed) / (Speed of the Boat in still water). 

Then the total time comes out to be

(Total Distance x Speed of the Boat in Still Water) / (Downstream Speed x Upstream Speed).

I have also solved three questions related to boats and streams in this video.

The questions discussed by me in this video are -

Question 1. Martin walked 1 km per hour slower than usual and he could return home in 9/8 of his usual time. His normal walking rate is ?

Question 2. A train after travelling 60 km meets with an accident and then proceeds at 3/4 of its former rate and arrives at the terminus 40 minutes late. Had the accident occurred 25 km further on, it would have arrived 10 minutes sooner than the previous case. Find the speed of the train and the total distance travelled ?

Question 3. The average speed of a bus is 20 percent less on the return journey than on the onward journey. The bus halts for half an hour at the destination bus stand before starting the return journey. If the total time taken for to and fro journey was 23 hours, covering a total distance of 1000 km, the average speed of the train on the return journey was how much ?

Question 4. X and Y start running towards each other at 6 km per hour and 9 km per hour respectively. What was the distance between them when they started if they met after 16 minutes ?

Question 5. A cycle, covers a distance of 80 km in 10 hours. If half the distance is covered in 3/5th of the time, then what will be the speed of the cycle to cover the rest of the distance in the remaining time ?

Question 6. To cover 600 km train T1 takes 8 hours more than train T2. If however, speed of the train T1 is doubled it takes two hours less than train T2. The speed of the train T2 in km per hour is ?

Question 7. A train with velocity 90 km per hour crosses a bridge in 36 seconds. Another train 100 meters shorter crosses the same bridge at 45 km per hour. Find the time taken by second train to cross the bridge ?

Question 8. A train 75 meters long overtook a man who was walking at the rate of 6 km per hour and crossed him in 18 seconds. Again, the train overtook a second person in 15 seconds. At what rate was the second person travelling ?

Question 9. Two trains of lengths 190 meter and 210 meter respectively, are running in opposite directions on parallel tracks. If their speeds are 40 km per hour and 32 km per hour respectively, in what time will they cross each other ?

Question 10. Two trains, 130 meter and 110 meter long, are going in the same direction. The faster train takes one minute to pass the other completely. If they are moving in opposite directions, they pass one another completely in three seconds. Find the speed of both the trains ?

Question 11. A man can row at the speed of 4.5 km per hour in still water to a certain upstream point and back to the starting point in a river which flows at 1.5 km per hour. Find the average speed for the total journey ?

Question 12. A man rows 10 km upstream and back again to the starting point in 55 minutes. If the speed of the stream is 2 km per hour, find the speed of rowing in still water ?

Question 13. A motor boat can travel at 10 km per hour in still water. It travelled 91 km downstream in a river and then returned, taking altogether 20 hours. Find the speed of the river flow ??