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Important Formulae

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.

Practice Questions

1.

 A boat travels 24 km upstream in 6 hours and 20 km downstream in 4 hours. Find the speed of the boat in still water and the speed of water current? A.4.5 kmph , 0.8 kmph B.3.5 kmph , 0.4 kmph C.3.6 kmph , 0.2 kmph D.4.5 kmph , 0.5 kmph

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.

 A man can row 8 km in one hour in still water. If the speed of the water current is 2 kmph and it takes 3 hours for him to go to a new place and return, find the distance from the starting point to the new place? A.11.25 km B.12 km C.12.25 km D.12.50 km

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.

 A man rows a distance of 4 km in 1 hour in still water and in 45 minutes with the current water. Find the time taken by him to row to 10 km with the current and return to the starting point? A.5 hours 37.5 min B.6 hours 36 min C.5 hours 35 min D.6 hours 37.5 min

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.

 A boat can travel 1.5 times the distance down the stream than up the stream in the same time. If the speed of the current is 3 kmph, Find the speed of the boat in still water? A.14 kmph B.15 kmph C.16 kmph D.17 kmph

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.

 A man can row (2/7)th of a kilometer upstream in 25 min and return 10 min. Find the speed of the man in still water? A.1 kmph B.1.2 kmph C.1.4 kmph D.1.6 kmph

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 can row a boat in still water at a speed of 6 kmph. If the speed of the stream is 2 kmph, then in how many hours will he row a distance of 24 km with the stream? A.2 B.4 C.6 D.3

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.

 A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water? A.4 kmph B.6 kmph C.8 kmph D.Data inadequate

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.

 A boatman goes 2 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 5 km in stationary water? A.40 minutes B.60 minutes C.75 minutes D.90 minutes

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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