A river is flowing at a speed of 5 km/h in a particular direction. A man, who can swim at a speed of 20 km/h in still water, starts swimming along the direction of flow of the river from from points A and reaches another point B which is at a distance of 30 km from the starting point A. On reaching point B, the man turns back and starts swimming against the direction of flow of the river and stops after reaching point A. The total time taken by the man to complete his journey is?

Let the speed of rowing in still water be u km/h.
Distance in downstream motion = 21 km
and speed downstream = (u + 4) km/h
? Time taken = 21/ (u + 4)
Distance upstream motion = 21 km and speed upstream = (u +4) km
? Time taken = 21/(u - 4)

According to the question.
21/(u + 4) + 2 = 21/(u - 4)
? (21 + 2u + 8)/u + 4 = 21/(u - 4)
? (2u + 29)/(u + 4) = 21/(u - 4)
? (u - 4) (2u + 29) = 21(u + 4)
? 2u² - 8u + 29u - 116 = 21u + 84
? 2u² + 21u - 116 = 21u + 84
? 2u² = 84 + 116
? u² = 200/2
? u² = 100
? u = 10 km/h

Let boatman's speed upstream x
And his speed downstream = 2x
? Ratio = (Speed in still water) : (Speed of stream)
= (2x + x/2) : (2x - x/2)
= 3x/2 : x/2
= 3 : 1

Speed of a boat in still water = distance / time = 12/1 = 12 km/h
Speed against the current = 12/3 km/h
Let the speed of the current = x km/h
According to the question,
12 - x = 4
? x = 8 km/h

Let rate of stream be 'a' km/h.
According to the question.
24 + a = 2(24 - a)
? 24 + a = 48 - 2a
? 3a = 48 - 24 = 24
? a = 24/3 = 8 km/h

Let speed of water current be x km/h
? Speed downstream = (10 + x) km/h.
Speed upstream = (10 - x) km/h
According to the question,
24/(10 + x) + 24/(10 - x) = 5
? 24[10 - x + 10 + x] = 5(10² - x²)
? 100 - x² = (24 x 20) / 5
? 100 - x² = 96
? x² = 4
? x = ?4 = 2km/h

Let speed of Ishwar's boat in still water be x km/h
and speed of current = y km/h
Rate downstream = (x + y) km/h
Rate upstream = (x - y) km/h
Let the distance covered in each case be a.
According to the question,
2a/(x + y) = a/(x - y)
? 2(x - y) = x + y
2x - 2y = x + y
? x = 3y
? x/y = 3/1
? x : y = 3 : 1

Let the distance be L km.
Speed of the main in still water = 7¹/₂ km/h
and speed of the river = 15 km/h

? Speed of the man downstream = 7.5 + 1.5 = 9
Speed of the man upstream = 7.5 - 1.5 = 6 km/h

According to the question,
L/9 + L/6 = 50/60
? (4L + 6L)/36 = 50/60
? 10L/36 = 50/60
? L = (50 x 36)/(10 x 60)
5? x = 3 km

Let speed of a motorboat be = 36k km/h
and speed of the current = 5k km/h
? Speed downstream = (36 + 5)k = 41k km/h
and speed upstream = (36 - 5)k = 31k km/h

Let distance be D km.
According to the question
When boat goes along with the current.
Distance = Time x Speed
? D = (5 + 10/60) x 41k
? D = 31/6 x 41k ....(i)

Again, when boat come back
a = Time x Speed
From Eq. (i) .
31/6 x 41k = Time x 31k
? Time = 41/6
Time = 6 h 50 min.

Given, downstream speed = 9 km/h
and upstream speed = 5 km/h

According to the formula
Ravi's speed in still water = (Speed downstream + Speed upstream )/2
= 1/2(9 + 5) = 14/2 = 7 km/h
and speed of current = (Speed downstream - Speed upstream)/2
= (9 - 5)/2 = 4/2 = 2 km/h.

Let the speed of boat and steam be x and y km/h.
? Speed of boat along steam = (x + y) km/h
and speed of boat against stream = (x - y) km/h

According to the question,
x + y = 1 / (5/60) = 60/5
? x + y = 12 ...(i)
and y - x = 6 ...(ii)

On adding Eqs. (i) and (ii), we get
2x = 18
x = 18/2 = 9

On putting the value of x in Eq. (i), We get
9 + y = 12
y = 12 - 9 = 3

Hence, speed of boat = 9 km/h
and speed of steam = 3 km/h