. A streamer goes downstream from one port to another in 6 hours. It covers the same distance upstream in 7 hours. If the speed of the stream be 2 km/hr, find the speed of the streamer in still water.
Answers
Answer: Let the speed of the streamer be x km/hr
Speed of Stream = 2 km/hr
It is given that while going downstream, the streamer takes 6 hours to cover the distance between two ports.
Speed of the streamer downstream = (x+2) km/hr
Distance Covered in 1 hour = (x+2) km
Distance covered in 6 hours =6(x+2) km
Distance between 2 ports = 6(x+2) km ....(i)
It is given that while going,upstream the streamer takes 7 hours to cover the distance.
Speed of Streamer Upstream = (x-2)km/hr
Distance covered in 1 hr = (x-2)
Distance covered in 7 hrs = 7(x-2) km
Distance between two ports in this case = 7(x-2) km ....(ii)
The distance between two ports is the same.
From (i) and (ii) we get,
Speed downstream = ( x + 2) km/hr
Distance = speed x time
Distance upstream = ( x - 2) 7
= 7x - 14 km
Distance downstream = (x + 2 ) 6
= 6x + 12 km
ATQ : distance upstream = distance downstream
So, 7x - 14 = 6x + 12
7x - 6x = 12 + 14
X = 26 km / hr
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