A man can row 7 ¹/ ₂ km/h in still water. If in a river running at 1.5 km/h, it takes him 50 min to row to a place and back, how far off is the place?

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

Given,
Speed of the stream = 5 km/h
and speed of the man in still water = 20 km/h
? Speed of the man downstream = 20 + 5 = 25 km/h
and speed of the man upstream = 20 - 5 = 15 km/h
? Total time taken to complete the whole journey = 30/25 + 30/15
= (30 x 8) / 75
= 3 h 12 min

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 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

? D/(8 - 2) + D/(8 + 2) = 32/60
? D/6 + D/10 = 32/60
? 10D + 6D = 32
? D = 2 km

Let the speed upstream be U km/hr and the speed downstream be V km/hr respectively.
Then 24/U + 36/V = 6 ...(i)
and 36/U + 24/V = 13/2 ...(ii)

Solving these 2 equations we get
? U = 8 km/hr and V = 12 km/hr
? Velocity of current = (12 - 8)/2 km/hr = 2 km/hr