Question

A steamer goes downstream and covers the distance
between two ports in 9 hours, while it covers the same distance upstream in 10 hours. If the speed of the stream is 1
km/hr, find the speed of the steamer in still water and the
distance between the two ports.

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Answer 1

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Given,

A steamer goes downstream and covers the distance  between two ports in 9 hours, while it covers the same  distance upstream in 10 hours. Speed of the stream is 1  km/hr.

To find :

Find the speed of the steamer in still water and the  distance between the two ports.

Solution :

Let the speed of streamer in still water be n km/h

Speed of stream = 1 km/h

∴ Speed of streamer in downstream = (n + 1) km/h

∴ Distance covered in downstream = 9(n + 1) km

Now, speed of streamer in upstream = (n - 1) km/h

∴ Speed of streamer in upstream = 10(n - 1) km

Now atq,

⇒ 9(n + 1) = 10(n - 1)

⇒ 9n + 9 = 10n - 10

⇒ 10n - 9n = 10 + 9

⇒ n = 19 km/h

∴ Speed of streamer in still water = 19 km/h

Now distance covered in upstream :

⇒ Distance b/w two ports = 10(19 - 1) km

⇒ Distance b/w two ports = 10 * 18

⇒ Distance b/w two ports = 180 km

∴ Distance between two ports = 180 km

Answer 2

Answer:

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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.is ur answer..