Downstream/Upstream:
In water, the direction along the stream is called downstream. And, the direction against the stream is called upstream.
1. If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then:
Speed downstream = (u + v) km/hr.
Speed upstream = (u  v) km/hr.
2. If the speed downstream is a km/hr and the speed upstream is b km/hr, then:
Speed in still water = 1/2(a + b) km/hr.
Rate of stream = 1/2(a  b) km/hr.
1. 

Upstream speed = 24/6 = 4 kmph.
Downstream speed = 20/4 = 5 kmph.
∴ speed in still water = (4 + 5)/2 = 4.5 kmph.
and, speed of water current = (5 – 4)/2 = 0.5 kmph.
2. 

Let the distance be X km.
Upstream speed = 8 – 2 = 6 km.
Downstream speed = 8 + 2 = 10 kmph.
Total time = time taken upstream + time taken downstream
⇒ Total time = X/6 + X/10 = 3 (given)
⇒ 16X/60 = 3
⇒ X = 180/16
⇒ X = 11.25 km
3. 

Speed in still water = 4/1 = 4 kmph
speed with the stream = 4/(4/3) = 16/3 = 5+1/3 km
∴ speed of water current = (16/3) – 4 = 4/3
∴ speed against the stream = 4 – 4/3 = 8/3
Hence, time taken to travel 10 km and back = 10/(16/3) + 10/(8/3)
∴ = 30/16 + 30/8 = 90/16 = 5 hours 37.5 min
4. 

If the distance covered down the stream is 1.5 times that covered up the stream, the speed down the stream will also be 1.5 times the speed up the stream.
Let the speeds of the boat in still water be u kmph.
We get, (u + 3)/(u – 3) = 3/2
⇒ u = 15 kmph
5. 

Upstream speed = (2/7)/(25/60) = 24/35 kmph
Downstream speed = (2/7)/(10/60) = 12/7 mph
speed in still water = [(24/35) + (12/7)]/2 = (84/35)X(1/2) = 1.2 kmph
6. 

Ajay is travelling with the stream.
∴ The relative speed is (6 + 2) kmph = 8 kmph
∴ The time taken to row 24 km distance
⇒ time = 24/8 = 3 hours
7. 

Rate downstream = (16/2) kmph = 8 kmph.
Rate upstream = (16/4) kmph = 4 kmph.
∴ Speed in still water = 1/2 x (8 + 4) kmph = 6 kmph.
8. 

Rate downstream = (1/10 x 60) kmph = 6 kmph.
Rate upstream = 2 kmph.
Speed in still water = 1/2 x (6 + 2) kmph = 4 kmph.
∴ Required time = (5/4) hrs = 1.25 = 75 min.
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