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Station 1, Station, 2 and station 3 are three towns on a river which flows uniformly. Station 2 is equidistant from station 1 and station 3. A man rows a boat from station 1 to station 2 and back in 17 hours. He can row from station 1 to station 3 in 7 hours. Find the ratio between the speed of boat in still water to the speed of flow of water?

Station 1, Station, 2 and station 3 are three towns on a river which flows uniformly. Station 2 is equidistant from station 1 and station 3. A man rows a boat from station 1 to station 2 and back in 17 hours. He can row from station 1 to station 3 in 7 hours. Find the ratio between the speed of boat in still water to the speed of flow of water? Correct Answer 17 : 10

Given:

Time taken to travel from Station 1 to station 3 = 7 hours

Total time taken from station 1 to station 2 and back to station 1 = 17 hours

Station 2 is equidistance from station 1 and station 3

Formula used:

Speed = Distance / Time

Calculation:

Clearly man travels downstream from station 1 to station 3 because time consumed is lesser

Since flow is uniform, so journey between station 1 to station 3 can be described as :

Time taken between station 1 to station 3 = time taken from station 1 to station 2 + time taken from station 2 to station 3

7 = time taken from (station 1 to station 2 + station 2 to station 3)     ---(i)

Since station 2 is equidistance from station 1 and 3

Therefore, time taken from station 1 to station 2 = time taken from station 2 to station 3

Therefore, 2 × time taken from station 1 to station 3 = 7

Time taken from station 1 to station 2 = 7 / 2 = 3.5 hours

Time taken from station 2 to station 1 = 17 - time taken between station 1 to station 2

= 17 - 3.5 = 13.5 hours

Let speed of boat in still water be ‘x’ and speed of current be ‘y’

Speed of boat in downstream = (x + y)

Speed of boat in upstream = (x -y)

(time taken to travel from station 1 to station 2) / (time taken from station 2 to station 1) = (3.5 / 13.5)

Since distance between station 1 and station 2 is fixed So time is inversely proportional to speed

(Speed of boat from station 2 to 1 (upstream)) / (speed of boat from station 1 to 2 (downstream)) = (3.5 / 13.5)

(x- y) / (x + y) = (3.5 / 13.5)

((x / y) -1) / ((x / y) + 1) = 3.5 / 13.5

Therefore, x / y = 17 / 10

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