TIPS TRICKS AND SHORTCUT METHOD TO SOLVE BOATS AND STREAMS

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Also we are coming daily with different topics and if you haven’t checked our latest articles on the Problems based on Races, Please Click the Below link to learn.

Problems based on Races

We have come up with Boats and Streams topics today.There are 5 types of problems asked in Boats and Streams.If we practice all these 5 types then we can solve any question asked in the exam.

Terms Related to Boats and Sreams:

                  Speed of the boat:It refers to the velocity of the boat in standing water ,let it be X.

                   Speed of the Stream: It refers to the velocity at which the water flows,let it be Y.

                   Upstream Speed (U): It is expressed as the (Speed of the Boat – Speed of the Stream) =X-Y. They row the boat in  the opposite direction to the flow of the stream.

                   Downstream Speed (D): It is expressed as the (Speed of the Boat + Speed of the Stream) =X+Y. They Row along the flow of Stream.

                    Speed of the boat in still water when upstream and downstream speed is given=1/2(D+U)

#.1 TYPE 1:

BASED ON TIME, SPEED AND DISTANCE:

  1. A boat can travel with a speed of 13km/hr in still water. If the speed of the stream is 4km/hr.Find the time taken by the boat to go 68km downstream?
Explanation:

Speed of the boat in still water(X)=13km/hr,

Speed of the stream(Y)=4km/hr.

Relative Speed of the boat in downstream=X+Y        17km/hr

                 Time=Distance/Speed

Time=68/17=4hrs

 2.A motorboat ,whose speed is 15km/hr in still water goes 30 km downstream and comes back in a total of 4hrs30mins.The speed of the stream in(km/hr)?

Explanation:

Speed of the Boat in Still Water(X)=15km/hr,

Time T=4hr 30min(for DownStream+UpStream)

Let the speed of the Stream=Y.

DownStream Speed=Speed of Boat +Speed of the Stream

=15+Y

UpStream Speed=Speed of the Boat-Speed of the Stream

=15-Y

                       Time =Distance/Speed

Time =4hr 30min=9/2hr

(9/2)=(30/(15+Y) + 30/(15-Y))

9/2=900/(225-Y^2)

Y=5

Speed of the Stream=5km/hr.

#.2 TYPE 2:

BASED ON RATIO:

1.A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat in still water and the  stream is?

Explanation:

Let the man’s upstream speed be X

Man’s downstream speed be 2x

Speed of the boat in still water when upstream and downstream speed is given=1/2(D+U) Speed of the stream =1/2(D-U)

Speed of the Boat Speed of the Stream
=½(2X+X)

=3X/2

=3

 ½ (2X-X)

=X/2

1

The ratio between speed of the boat to the speed of the stream=3:1

#.3 TYPE 3:

BASED ON EFFICIENCY:

1.A man can row 12km/hr in still water .He finds that it takes him thrice as much time to row up the river as it takes to row down the river.What is the  speed of the current?

Explanation:

Let the distance be D,

Speed of the boat in still water=12km/hr.

Speed of the current=Ykm/hr

Time taken during Upstream Time taken during downstream
3 1

Distance =Time *Speed

upstream=3*(12-Y){ Speed of the Boat – Speed of the Stream}

Downstream=1*(12+Y){ Speed of the Boat +Speed of the Stream}

Distance is same here

3*(12-Y)=12+Y

36-3Y=12+Y

4Y=24

Y=6km/hr

Speed of the Stream=6km/hr

# 4.TYPE 4:

SOLVING BY EQUATIONS:

1.A person can row 18km downstream and 27km upstream in three hours and 18km upstream and 27km downstream in 2hours 42minutes.What is the upstream and Downstream Speed?

Explanation:

Downstream D=X+Y  Upstream U=X-Y

Therefore,

18D+27U=3

27D+18U=27/10

Solving   above  we get U=2/25  and   D=14/300

# 5.TYPE 5:

BASED ON AVERAGES:

1.A Man can row at a speed of 5km/hr in still water to a certain distance  upstream and back to the starting point in ariver,which flows at 2km/hr.Find the average speed for the total journey?

Explanation:

Average when  2 speeds are given for travelling the same distance too and fro then the average speed =2DU/(D+U)

Where D=Speed when travelling Downstream,U=Speed when travelling Upstream.

Downstream Speed=Speed of the Boat + Speed of the Stream .D=5+2=7km/hr

Upstream Speed =Speed of the Boat – Speed of the Stream.U=5-2=3km/hr

Average Speed=2*7*3

2*7*3     42
3+7         10

4.2km/hr

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