A streamer goes downstream from one port to another in 6 hours. It covers the same distance in upstream in 7 hours. If the speed of the stream is 2km/hr, find the speed of the streamer in still water.
Answers
Answer:
Let speed of the streamer in still water= x km/hr
Speed of downstream =(x+2)km/hr
Distance between the ports =4(x+2)km.... (i)
Speed of upstream =(x-2)km/hr
Distance between the ports =5(x−2)km....(ii)
from Equation (i) and (ii)
4(x+2)=5(x−2)
4x+8=5x−10
x=18
∴ Distance between two ports =4(x+2)
=4(18+2)km=80 km
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Let the speed of the streamer in still water be x km/hr.
Speed of the streamer = 2km/hr
It is given that while going downstream, the streamer takes 6 hours to cover the distance between two ports.
Therefore, speed of the streamer downstream
= (x + 2)km/hr
Distance covered in 1 hr = (x + 2)km
Distance covered in 6 hrs= 6 (x + 2)km
Therefore, Distance between two ports = 6( x + 2)km---------(i)
It is given that while going upstream, the streamer takes 7 hours to cover the distance.
Speed of the streamer upstream = (x - 2)km/hr
Distance covered in 1 hr = ( x - 2)km
Distance covered in 7 hrs = 7 (x -2)km
Therefore, distance betweentwo ports in this case = 7(x - 2)km---------(ii)
The distance between two ports is the same.
From (i) and (ii), we get
➨ 6 (x + 2) = 7 (x - 2)
➨ 6x + 12 = 7x - 14
➨ 6x - 7x = -14 - 12
➨ -x = -26
➨ x = 26
Therefore, the speed of the streamer in still water = 26km/hr
Verification :
Speed of the streamer downstream = (26+2)km/hr = 28km/hr
Speed of the streamer upstream = (26-2)km/hr = 24km/hr
Distance covered in 6 hrs while going downstream = (6× 28)km = 168km
Distance covered in 7 hrs while going upstream = (7× 24)km = 168km
Hence, both the distance are equal.
Therefore, solution is verified.