Question

a streamer goes downstream from one station to another in 9 hours it cover the same distance upstream in 10 hours if the speed of the stream be 1 kilometre per hour find the speed of the stream

Answer 1

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Given,

Speed of the stream = 1 km/hr

Let the speed of steamer in still water be xkm/hr.

Speed of the steamer downstream = Speed of steamer in still water + Speed of the stream = (x + 1) km/hr

Speed of the steamer upstream = Speed of steamer in still water – Speed of the stream = (x – 1) km/hr

Distance covered by the steamer downstream in 9 hours = 9 (x + 1) km (. :

 Distance = Speed × Time)

Distance covered by the steamer upstream in 10 hours = 10 (x – 1) km.

Distance covered by steamer downstream in 9 hours = Distance covered by steamer upstream in 10 hours

∴ 9 (x + 1) = 10 (x – 1)

⇒ 9x + 9 = 10x – 10

⇒ 9x – 10 = – 10 – 9

⇒ – x = – 19

⇒ x = 19

∴ Speed of steamer in still water is 19 km/hr.


=> Distance between the two ports = 9 ( x + 1)

=> 9 ( 19 + 1)

=> 9 × 20

=> 180 km.
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Answer 2

Let the speed of steamer = x km/hr
speed of stream = 1 km/hr
so down stream resultant speed = (x + 1) km/hr
& up stream resultant speed = (x – 1) km/hr
Distance = speed × time
= 9 (x + 1) = 10 (x – 1)
9 x + 9 = 10 x – 10
x = 10 + 9 = 19 km/hr.
Therefore, The speed of the streamer in still water is 19 km/hr.

Distance travelled = 9(s + 1) = 9 × 20 = 180 km (If necessary).

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