ied.
Example 10: A steamer goes downstream from one port to another in 6 hours. It cover
the same distance upstream in 7 hours. If the speed of the stream be 2 km/hr, find th
speed of the steamer in still water.
Answers
Answer:
26km/h
Step-by-step explanation:
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.
\therefore∴ 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
\therefore∴ 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
\therefore∴ Distance between two ports in this case = 7(x-2) km ....(ii)
\because∵ The distance between two ports is the same.
\therefore∴ From (i) and (ii) we get,
\implies\: 6(x + 2) = 7(x - 2)⟹6(x+2)=7(x−2)
\implies \: 6(x + 2) = 7(x - 2)⟹6(x+2)=7(x−2)
\implies \: 6x + 12 = 7x - 14⟹6x+12=7x−14
\implies \: - x = - 26⟹−x=−26
\implies\: x = 26⟹x=26
\therefore∴ The speed of the streamer in still water = 26km/hr
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