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In 9 hours, a riverboat travels downstream from one port to another. In 10 hours, it travels the same distance upstream. Find the steamer's speed in calm water and the distance between the ports if the stream is moving at $1 k m / h$ .

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19 k m / h, 180 k m

18 k m / h, 190 k m

9 k m / h, 880 k m

10 k m / h, 190 k m

answer is A.

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Detailed Solution

Given that, a riverboat travels downstream from one port to another in 9 hours.
It travels the same distance upstream in 10 hours.
Speed of stream

= 1 k m / h

.
Let speed of riverboat in calm water

= x k m / h

.
Time taken by riverboat to go downstream from one port to another,

t (d s) = 9 h r

.
Time taken by riverboat to go upstream from one port to another,

t (u s) = 10 h r

.
Total speed of riverboat going downstream = speed of riverboat in calm water + speed of stream.

⇒ s (d s) = (x + 1) k m / h

U s i n g, s p e e d = d i s t a n c e t i m e :

⇒ s (d s) = d t (d s)

⇒ (x + 1) = d 9 ⇒ 9 (x + 1) = d

⇒ d = 9 x + 9

-(i)
Total speed of riverboat going upstream = speed of riverboat in calm water - speed of stream.

⇒ s (u s) = (x − 1) k m / h

U s i n g, s p e e d = d i s t a n c e t i m e :

⇒ s (u s) = d t (u s)

⇒ (x − 1) = d 10 ⇒ 10 (x − 1) = d

⇒ d = 10 x − 10

-(ii)
As we know that distance between ports while going downstream and upstream is same,
Equating equation (i) & (ii),

⇒ 9 x + 9 = 10 x − 10 ⇒ 9 x − 10 x = − 10 − 9 ⇒ − x = − 19

⇒

x = 19 k m / h

Substituting value of ‘x’ in equation (i),

⇒ d = 919 + 9 ⇒ d = 171 + 9 ⇒ d = 180 k m

Speed of streamer in still water

= 19 k m / h

.
Distance between the ports

= 180 k m

.
Hence, option 1 is correct.

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