Concept of “Boat and Stream”-02

Question: Ramesh can row a certain distance downstream in 6 hrs and return the same distance in 9 hrs. If the stream flows at the rate of 3 km/h, find the speed of Ramesh in still water. [Ans. (b) 15 km/hr]

(a) 6 km/h (b) 15 km/h (c) 8 km/h (d) 9 km/h (e) None of these

Solution: 

Detailed explanation: 

First Method: Let “X” and “Y” are the speeds of Ramesh along downstream and upstream respectively. Since distance is the same; so speeds will be in the inverse ratio of time taken.

Also, speed of a man downstream, X = u + v

And, speed of a man upstream, Y = u - v

So, X : Y = 9 : 6

It means (u + 3) : (u - 3) = 3 : 2 That is, (u + 3) / (u - 3) = 3 / 2. Or, u = 3 × 5 = 15 km/h Ans.

Second Method: Since distance is the same; so speeds will be in the inverse ratio of time taken.

Also, speed of a man downstream, X = u + v

And, speed of a man upstream, Y = u - v

So, X : Y = 9 : 6 = 3 : 2

u : v = X + Y : X – Y = 3 + 2 : 3 – 2 = 5 : 1

But, “1” is the speed of current and it is given as 3 km/h.

So, “3” is the speed of Ramesh, that must be 3 × 5 = 15 km/h Ans.

Third Method : We know that

Distance = speed × time

Downstream speed is X and time taken is 6 hours; while upstream speed is Y and time taken is 9 hours.

Also, X = u + v and Y = u - v

Therefore, (u + 3) × 6 = (u - 3) × 9

Or, (u + 3) × 2 = (u - 3) × 3

Or, u = 3 × 5 = 15 km/h Ans.

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