**Upstream:**In water, the direction against the stream is called upstream.**Downstream:**In water, the direction along the stream is called downstream.- Let the speed of a boat in still water be u km/hr and the speed of the stream be v km/hr, then:
- Speed downstream = (u + v) km/hr
- Speed upstream = (u - v) km/hr.

- Let the speed downstream be a km/hr and the speed upstream be b km/hr, then:
- Speed in still water =1/2(a+b) km/hr
- Rate of stream = 1/2(a−b) km/hr

- A man can row a boat in still water at x km/hr in a stream flowing at y km/hr. If it takes him t hours to row a place and come back, then the distance between the two places = t(x
^{2}−y^{2}) / 2x km - A man takes n times as long to row upstream as to row downstream the river. If the speed of the man is x km/hr and the speed of the stream is y km/hr, then x = y(n+1) / (n−1)

- A boat takes 28 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 6km/hr and the speed of the boat in still water is 9 km/hr, what is the distance between A and B?

A. 115 kms

B. 120 kms

C. 140 kms

D. 165 kms - Speed of a man in still water is 5 km/hr and the river is running at 3km/hr. The total time taken to go to a place and come back is 10 hours. What is the distance travelled?

A. 10 kms

B. 16 kms

C. 24 kms

D. 32 kms - A boat running upstream takes 9 hours 48 minutes to cover a certain distance, while it takes 7 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?

A. 5:2

B. 7:4

C. 6:1

D. 8:3 - A boat can travel 20 km downstream in 24 min. The ratio of the speed of the boat in still water to the speed of the stream is 4 : 1. How much time will the boat take to cover 15 km upstream?

A. 20 mins

B. 22 mins

C. 25 mins

D. 30 mins - A boat whose speed in 20 km/hr in still water goes 40 km downstream and comes back in a total of 5 hours. The approx. speed of the stream (in km/hr) is:

A. 6 km/hr

B. 9 km/hr

C. 12 km/hr

D. 16 km/hr - A boat covers a certain distance downstream in 2 hour, while it comes back in 2 1/2 hours. If the speed of the stream be 5 kmph, what is the speed of the boat in still water?

A. 40 kmph

B. 30 kmph

C. 35 kmph

D. 45 kmph - A boat running downstream covers a distance of 40 km in 5 hrs and for covering the same distance upstream it takes 10 hrs. What is the speed of the stream?

A. 5 km/hr

B. 2 km/hr

C. 6 km/hr

D. 4 km/hr - A boat goes 4 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 15 km in stationary water?

A. 2 hours

B. 2 hours 15 mins

C. 3 hours

D. 3 hours 30 mins - A man rows to a place 40 km distant and come back in 9 hours. He finds that he can row 5 km with the stream in the same time as 4 km against the stream. The rate of the stream is:

A. 1 km/hr

B. 1.5 km/hr

C. 2 km/hr

D. 2.5 km/hr - A man can row 8 km/hr in still water. When the river is running at 4 km/hr, it takes him 2 1/3hr to row to a place and come back. How far is the place?

A. 4 kms

B. 5 kms

C. 7 kms

D. 10 kms

Downstream speed = 9+6 = 15

Upstream speed = 9-6 = 3

Now total time is 28 hours

If distance between A and B is d, then distance BC = d/2

Now distance/speed = time, so

d/15 + (d/2)/3= 28

Solve, d = 120 kms

Down speed= 5+3= 8

Up speed= 5-3=2

Let distance travelled = X

(X/8)+(X/2)= 10

X = 16 kms

Total distance is 16+16 = 32 kms

Distance covered upstream in 9 hrs 48 min = Distance covered downstream in 7 hrs

(X-Y) 49/5 = (X+Y) 7

X/Y = 1/6

Down speed =20/24*60=50km/hr

4:1 =4x:x

Downstream speed = 4x+x=5x

Upstream speed = 4x-x=3x

5x= 50; x=10

so up speed 3*10=30

Time = 15/30*60= 30 mins

Let the speed of the stream be x km/hr. Then,

Speed downstream = (20 + x) km/hr,

Speed upstream = (20 – x) km/hr.

40/20+x + 40/20-x = 5

X = 9 km/hr appx.

Let the speed of the boat in still water be x kmph. Then,

Speed downstream = (x + 5) kmph,

Speed upstream = (x – 5) kmph.

(x + 5)*2 = (x – 5)*5/2

X = 45 kmph

Downstream speed = 40/5 = 8 km/hr

Upstream speed = 40/10 = 4 km/hr

So speed of stream = 1/2*(8-4)

Rate downstream = 1/10 * 60 = 6kmph

Rate upstream = 4 km/hr.

Speed in still water = ½ * 10 = 5 kmph

Required time = 15/5 = 3 hours

Speed downstream = 5/x

Speed upstream = 4/x

40/(5/x) + 40/(4/x) = 9

X = ½

So, Speed downstream = 10 km/hr, Speed upstream = 8 km/hr

Rate of the stream = 1/2 * 2 = 1 km/hr

Downstream speed = 8+4= 12 => a

Upstream speed = 8-4= 4 => b

Distance = a*b/(a+b) * total time (t)

= 12*4/16 * 7/3

= 7 kms

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