 Hello and welcome to this session. In this session, we discussed the following question which says, a streamer goes downstream from one port to another in 8 hours. It covers the same distance upstream in 10 hours. If the speed of the stream be 1 km per hour, find the speed of the streamer in still water and the distance between the ports. Now let's proceed with the solution. Since we need to find the speed of the streamer in still water, so we take, let the speed of the streamer in still water be equal to x km per hour. And we have the speed of the stream is given to be 1 km per hour. So we write, speed of the stream is equal to 1 km per hour. So the speed downstream would be equal to x plus 1 km per hour. The speed upstream is equal to x minus 1 km per hour. That is for the speed downstream, we have added the speed of the streamer in still water with the speed of the stream. And for the speed upstream, we have subtracted the speed of the stream from the speed of the streamer in still water. Now next we have the distance covered in 8 hours while going downstream is equal to speed into time. That is speed downstream x plus 1 into time that is 8. So the distance covered in 8 hours while going downstream is equal to x plus 1 into 8 km. In the same way, we find the distance covered in 10 hours while going upstream would be equal to the speed upstream that is x minus 1 into time that is 10 hours. So this distance would be x minus 1 into 10 km. Now according to the question we have that the distance covered upstream and downstream is same. But each of these distances is the distance between the two ports which is the same. Therefore we have x plus 1 into 8 is equal to x minus 1 into 10. This implies plus 8 is equal to 10x minus 10. Now we transpose this 10x to the left hand side. So we have 8x plus 8 is equal to minus 10 which gives us minus 2x plus 8 is equal to minus 10. Now we transpose this plus 8 to the right hand side. So we get minus 2x is equal to minus 10 minus 8 which gives us minus 2x is equal to minus 18. Now to get the value for x we divide both sides by minus 2. Now this minus 2 minus 2 gets cancelled and 2 9 times is 18. So we have x is equal to 9. And we had assumed the speed of the steamer in still water to be x km per hour. Thus we say still water is equal to 9 km. And the distance between is given by 8 into x plus 1 km x minus 1 km. Now putting the value for x we get this distance would be equal to 8 into 9 plus 1. That is 8 into 10 which is equal to 80 km. In this case also we would get 80. That is minus 1 when we put x as 9 we get 80. Since stream and upstream are equal as given in the question. So final answer is speed of the steamer in still water is 9 km per hour. And the distance between two ports is 80 km. This completes our session. Hopefully you understood the solution for the given question.