A boat has to travel upstream 20 km distance from point X of a river to points Y. The total time taken by boat in travelling from point X to Y and Y to X is 41 min 40 s. What is the speed of the boat?

Given, speed of boat = 10 km/h
Let speed of flow of river = x km/h
? Upstream speed of boat = (10 - x) km/h
and downstream speed of boat = = (10 + x) km/h

According to question.
91/(10 - x) + 91/(10 + x) = 20
? 91(10 + x + 10 - x) / (10 - x) (10 + x) = 20
? 91(20) / 100 - x² = 20
? 91 = 100 - x²
? x² = 9
? x = 3

Let the distance between M and N and the speed of current be d km and x km/hr respectively.
According to the question = {d/(4 + x) + d/(4 - x)} = 3

In the above equation we have only one equations but two variables. Hence cannot be determined (Data inadequate).

Speed upstream = (6 - 1.5) km/hr = 4.5 km/hr
Speed downstream = (6 + 1.5) km/hr = 7.5 km/hr
Total time taken = (22.5/4.5 + 22.5/7.5) hrs
= (5 + 3) hrs.
= 8 hrs.

Suppose he moves 4 km downstream in H hrs.
Then, Speed downstream = 4/H km/hr
Speed upstream = 3/H km/hr

T₁ + T₂ = 14
? (48 x H)/4 + (48 x H)/3 = 14
? 12H + 16H = 14
? H = 1/2

? Speed downstream = 8 km/hr
Speed upstream = 6 km/hr
? Rate stream = (8 - 6)/2 km/hr = 1 km/hr

Let the speed in still water be x km/hr
? 35/(x - 1) + 35/(x + 1) = 12
? 35(2x) = 12(x² - 1)
? 12x² - 70x - 12 = 0
? 12x² - 72x + 2x - 12 = 0
? 12x(x - 6) + 2 (x - 6) = 0
? (x - 6) (12x + 2) = 0
? x = 6 km/hr

Let speed of stream be x km/h
Given speed of motorboat in still water = 45 km/h
? Speed of boat along stream = (45 + x) km/h

According to the question,
45 + x = 80 x 1¹/₃
? 45 + x = 80 x 3 / 4
? x = 60 - 45 = 15
? Speed of boat against stream = 45 - 15 = 30 km/h
Hence, required time = Distance / Speed = 80 / 30
= (8 x 60)/3 = 160 min
= 2 h 40 min

Let the distance be D km.
Speed download = (5 +2) = 7 km/h
and speed upstream = (5 -2) = 3 km/h
According to the question,
D/3 - D/7 = 2
? 7D - 3D = 21 x 2
? D = (21 x 2)/4 = 10.5 km

Let velocity of the stream be x km/h
? Velocity of the boat downstream = (4 + x) km/h
and velocity of the boat upstream = (4 - x) km/h
According to the question, 3(4 + x) = 9(4 - x)
? 12 + 3x = 36 - 9x
? 12x = 24
? x = 2 km/h

Speed upstream = 10 / (30/60) = (10 x 60)/30 = 20 km/h
Speed downstream = 10/(25/60) = (10 x 60)/25 = 24 km/h
? Speed of the river's current = (24 - 20)/2 = 4/2 = 2 km/h

Let the distance between the two ports be x km.
Then, speed downstream = x/4
And speed upstream = x/5
? Speed of the stream = [speed downstream + speed upstream] / 2 = (x/4 - x/5)/2
? (5x -4x)/40 = 2
? x/40 = 2
? x = 80 km