Given: Time taken by boat to cover 28 km upstream and 28 km downstream = 13 hours 20 minutes Time taken by boat to cover 7 km downstream = Time taken by boat to cover 3 km upstream Concept Used: If 'b' is the speed of a boat and 's' is the speed of a stream then, Upstream speed of boat = b - s Downstream speed of boat = b + s Formula used: Time = Distance/Speed Calculation: Let the speed of the boat be 'b' and the speed of the stream be 's'. According to the question, {28/(b - s)} + {28/(b + s)} = (13 + 20/60) = 40/3 ----(i) {3/(b - s)} = {7/(b + s)} ----(ii) From equation(ii): {3/(b - s)} = {7/(b + s)} ⇒ 3(b +s) = 7(b - s) ⇒ 3b + 3s = 7b - 7s ⇒ 3b - 7b = -7s - 3s ⇒ - 4b = -10s ⇒ b/s = 5/2 Let the speed of boat be 5x km/hr The speed of stream be 2x km/hr From equation(i): {28/(b - s)} + {28/(b + s)} = 40/3 ⇒ {28/(5x - 2x)} + {28/(5x + 2x)} = 40/3 ⇒ 28/3x + 28/7x = 40/3 ⇒ 28{(7x + 3x)/21} = 40/3 ⇒ 28 × 10x/21 = 40/3 ⇒ 40x/3 = 40/3 ⇒ x = 1 km/hr The speed of boat (b) = 5x km/hr = 5 × 1 = 5 km/hr The speed of stream (s) be 2x km/hr = 2 × 1 = 2 km/hr Upstream speed of boat = b - s = 5 - 2 = 3 km/hr ∴ The speed (in km/h) of the boat when going upstream is 3 km/hr. Additional Information 1) Upstream: The boat or a swimmer moving against the stream is known as moving upstream (against the flow of water). 2) Downstream: The boat or a swimmer moving along the stream is known as moving downstream (along the flow of water). 3) If the speed of the boat or swimmer is X km/hr and the speed of the stream is Y km/hr, a) The speed of the boat or swimmer in the direction of the stream is known as speed downstream. It is given by; Speed downstream = (X + Y) km/hr b) And, the speed of the boat or swimmer against the stream is known as speed upstream. It is given by; Speed upstream = (X - Y) km/hr