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Boats and Streams

Shortcut Tricks on Boats & Streams:

Boat Speed in still water (water is not moving) = ‘u’ kmph

Speed of the stream(moving water speed) = ‘v’ kmph

Down Stream= u + v = a kmph.

Up Stream = u – v = b kmph.

Speed of the stream(flowing water or speed of current) =  ½(a-b)

Speed of boat in still water =  ½(a+b)

Problem 1:

A boat 90 mins less to travel 36km downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 kmph. What is the speed of stream?

Sol:               Here , Distance = constant.

 

 UpstreamDownstream
Speed 10-s10+s
Timed/10-sd/10+s

Difference in time=Upstream Time-Downstream Time

(90/60)hrs= d/10-s  – d/10 +s

3/2 hrs=   (360+36s-360+36s)/100S2

300-3S2= 144S

S=2kmph.

Problem 2:  A man takes as long as to row a distance against the stream  as to row to the same distance in favour of the stream . The ratio of the speed of boat and speed of the current?

Sol:

Sb(boat speed)            Sc(stream)       D(distance)     T( time)

Given,  T(upstream) = 2 T(downstream)  Find Sb/Sc

Downstream Time = Tdwn = D/(Sb+Sc)

Upstream Time = Tup = D/(Sb_Sc)

Substitute this in the given info i.e. T(upstream)=T(downstream)

D/ (Sb-Sc) = 2 D/(Sb+Sc)

Sb+Sc = 2Sb-2Sc

3Sc=Sb

Sb/Sc=3/1

 

Problem 3:

A boat covers certain distance downstream 1 hour and while it comes back in 1 ½ hr. If Sc=3 kmph and Sb=?

Sol:

Here, Distance = Const.(same)

Distance of Upstream = Distance of  Downstream

(Sb-3)3/2 hrs = (Sb + 3) *1

3 Sb – 9 = 2Sb +6

Sb = 15.

Problem 4:

A motor boat Speed is 15 kmph in still water goes 30 km downstream and comes back in total 4 hrs 30 mins . What is the speed of stream ?

Sol:

Sb=15,                Sc=? ,                D= 30km,            T=4 ½ hrs=9/2 hrs,

Time = Tupstream + Tdwnstream

9/2  = 30/ (15-Sc)  +  30/(15+Sc)

9/2 =  450+30Sc +450 – 30Sc

225- S2c

= 9(225- S2c) = 2(900)

S2c = 25

Sc =5

 

 

 

 

 

 

 

 

 

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