Maths Course in English

Boats and Streams Formula and Questions

Boats and Streams Formula and Questions
Written by babajiacademy
In this page, you will learn about Boats and Streams Formula and Questions in English. This topic is very important for 2019 Exam preparation. So before proceeding for any exam read these short tricks and explanations carefully about Boats and Stream Questions.

Aptitude Boats and Streams Concepts

From this page, you can easily learn about boats and stream tricks and concept. So don’t waste your time just scroll down and learn the concept now. If you like this concept, then leave a comment below in the comment box.
  • Stream: It implies that the water in the river is moving or flowing.
  • Upstream: Going against the flow of the river.
  • Downstream: Going with the flow of the river.
  • Still water: It implies that the speed of water is zero (generally, in a lake) .

When we move upstream, our speed gets deducted from the speed of the stream. Similarly when we move downstream our speed gets added.

Let the speed of a boat in still water be A km/hr and the speed of the stream (or current) be B km/hr, then

  • Speed of boat with the stream = (A + B) km/hr
  • Speed of boat against the stream = (A – B) km/hr
  • Speed of boat in still water is:

boats-streams-f-22938.png boats-streams-f-22944.png

  • Speed of the stream or current is:

boats-streams-f-22950.pngboats-streams-f-22958.png

Quicker Method to solve the Questions

Boat’s speed in still water

=boats-streams-f-22964.png

Example 1: A boat travels equal distance upstream and downstream. The upstream speed of boat was 10 km/hr, whereas the downstream speed is 20 km/hr. What is the speed of the boat in still water?

Solution: Upstream speed = 10 km/hr

Downstream speed = 20 km/hr

As per formula, Boat’s speed in still water

boats-streams-f-22970.png

Therefore, Boat’s speed in still water

boats-streams-f-22976.png= 15

Speed of current

boats-streams-f-22983.png

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Example 2: A boat travels equal distance upstream and downstream. The upstream speed of boat is 10 km/hr, whereas the downstream speed is 20 km/hr. What is the speed of the current?

Solution: Upstream speed = 10 km/hr

Downstream speed = 20 km/hr

As per formula, Speed of current

=boats-streams-f-22989.png

Therefore, Speed of current

boats-streams-f-22995.png= 5 km/hr


Example 3: A boat is rowed down a river 28 km in 4 hours and up a river 12 km in 6 hours. Find the speed of the boat and the river.

Solution: Downstream speed is boats-streams-f-23001.png,

Upstream speed is boats-streams-f-23009.png = 2 kmph
Speed of Boat boats-streams-f-23015.png(Downstream + Upstream Speed)

boats-streams-f-23021.png kmph

Speed of current boats-streams-f-23028.png (Downstream–Upstream speed)

boats-streams-f-23034.png

A man can row X km/h in still water. If in a stream which is flowing of Y km/h, it takes him Z hours to row to a place and back, the distance between the two places is

boats-streams-f-23040.png

Example 4: A man can row 6 km/h in still water. When the river is running at 1.2 km/h, it takes him 1 hour to row to a place and back. How far is the place?

Solution: Man’s rate downstream = (6 + 1.2) = 7.2 km/h.

Man’s rate upstream = (6 – 1.2) km/h = 4.8 km/h.

Let the required distance be x km.

Then boats-streams-f-23046.png = 1

or 4.8x + 7.2x = 7.2 × 4.8

⇒ boats-streams-f-23055.png

By direct formula:

Required distance

boats-streams-f-23061.pngboats-streams-f-23069.pngkm

A man rows a certain distance downstream in X hours and returns the same distance in Y hours. If the stream flows at the rate of Z km/h, then the speed of the man in still water is given by

boats-streams-f-23075.png

And if speed of man in still water is Z km/h then the speed of stream is given by

boats-streams-f-23081.png

Example 5: Vikas can row a certain distance downstream in 6 hours and return the same distance in 9 hours. If the stream flows at the rate of 3 km/h, find the speed of Vikas in still water.

Solution: By the formula,

Vikas’s speed in still water

boats-streams-f-23087.png= 15 km/h

If a man capable of rowing at the speed u of m/sec in still water, rows the same distance up and down a stream flowing at a rate of v m/sec, then his average speed through the journey is

boats-streams-f-23096.png

boats-streams-f-23102.png

Example 6: Two ferries start at the same time from opposite sides of a river, travelling across the water on routes at right angles to the shores. Each boat travels at a constant speed though their speeds are different. They pass each other at a point 720 m from the nearer shore. Both boats remain at their sides for 10 minutes before starting back. On the return trip they meet at 400 m from the other shore. Find the width of the river.

Solution: Let the width of the river be x.

Let a, b be the speeds of the ferries.

boats-streams-f-23108.png… (i)

boats-streams-f-23114.png… (ii)

(Time for ferry 1 to reach other shore + 10 minute wait + time to cover 400m) = Time for freely 2 to cover 720m to other shore + 10 minute wait + Time to cover (x – 400m) )

Using (i) , we get boats-streams-f-23137.png

Using (ii) , boats-streams-f-23144.png

On, solving we get, x = 1760m

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