Question

A streamer goes downstream from one port to another in 9 hours and cover the same distance upstream in 10 hours.If the speed of the stream is 3 km/hr,find the speed of the streamer in still water and distance between the ports.​

Answer 1

Answer:

Step-by-step explanation:

Let the speed of the steamer in still water is x km/h and distance is d.  

Then, speed of steamer downstream (u)= speed of steamer in still water+speed of stream=x+1

Speed of steamer upstream (v)=speed of steamer in still water-speed of stream=x−1

Distance covered by steamer upstream (d)=10(x−1)          ......(1)

Distance covered by steamer downstream (d)=9(x+1)      ......(2)

From equation (1) and (2),

10 (x−1) = 9( x+1 )

10x − 10= 9x + 9

10x − 9x = 9 + 10

x = 19 km/h

Substituting this value in equation(1),

Distance (d) = 10 (19 −1 ) = 180km

Hence, the speed of the steamer in still water is 19km/h and the distance between the ports is 180km.

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Answer 2

Step By Step explaination.

Let the spread of the streamer in still water is x km/h and distance is d.

Then, speed of steamer downstream (u) = spread of streamer in still water+ speed = x-3

Distance covered by steamer upstream

(d) = 10(x-3) ....(1)

Distance covered by steamer downstream

(d) = 9(x+3) ...(2)

From equation (1) and (2)

10(x-3) = 9(x+3)

10x - 30 = 9x + 27

10x - 9x = 27 + 30

x = 57 km/ h.

Substituting the value in equation (1)

Distance(d) =. 10(57-3) = 540 km/h

Hence, the speed of the streamer in still water is 57 km/h and the distance between the ports is 540 km.