Q16 of 46 Page 175

A steamer goes down stream and covers the distance between two ports in 4 hours while it covers the same distance up stream in 5 hours. If the speed of the steamer upstream is 2 km/hour, find the speed of steamer in still water.

Let, the speed of the steamer in still water = x km/hr


Speed of the stream = y km/hr


Speed of the steamer in upstream = 2 km/hr


Time taken by the steamer to cover the distance in upstream = 5 hrs.


∴ Distance = 2 × 5 = 10 km


Time taken by the steamer to cover the distance in downstream = 4 hrs.


∴ Speed of the steamer in downstream = 10/4 = 2.5 km/hr


∴ x – y = 2 …… (1)


∴ x + y = 2.5 …… (2)


From (1) + (2) we get,


⇒ 2x = 2 + 2.5


⇒ x = 2.25


∴ Speed of the steamer in still water = 2.25 km/hr


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