A steamer goes downstream form one point to another in 6 hours. It covers the same distance upstream in 7 hours. If the speed of the stream is 2 km/hr, find the speed of the steamer 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,
6(x + 2) = 7(x - 2)⟹6(x+2)=7(x−2)
6(x + 2) = 7(x - 2)⟹6(x+2)=7(x−2)
6x + 12 = 7x - 14⟹6x+12=7x−14
x = - 26⟹−x=−26
x = 26⟹x=26
∴ The speed of the streamer in still water = 26km/h
Step-by-step explanation:
Given: Let the speed of steamer in still water be x km/hr. Speed of stream is 2 km/hr.
.:. Speed downstream (x + 2) km/hr and speed upstream (x - 2) km/hr
Now, considering downstream :
The distance covered in 1 hr - (x + 2) km.
.:. The distance covered in 6 hrs downstream - 6(x + 2) km
Similarly, considering upstream:
The distance covered in 1 hr - (x - 2) km
.:. The distance covered in 8 hrs upstream = 8(x - 2) km
Now, distance covered upstream is
same as distance covered downstream.
.:. 8(x-2) 6(x + 2)
=> 8x16- 6x + 12
=> 8x6r 12+ 16
=> 2r- 28 x 14
Hence, speed of steamer in still water is 14 km/hr.
Note : In upstream, always the difference of speeds of steamer and stream is considered. In downstream, always the sum of speeds of steamer and stream is considered.
