Boats & Streams - Fundamentals

• Important Facts and Formulae

First thing is : The speed of water or stream that denoted by v km/hr.
Second thing is : Speed of boat or boatman in calm water which we denoted by u km/hr.
Speed downstream = ( u + v ) km / hr
Speed upstream = ( u – v ) km / hr.
Third thing is : In water, the direction along with stream is called Downstream.
Four thing is : The direction of boat against the stream is called Upstream.
If the speed downstream is x km / hr and the speed upstream is y km / hr, then :
Speed in still water = 1 / 2 ( x + y ) km / hr
Rate of Stream = 1 / 2 ( x – y ) km / hr .

Example 1: A boat man covers a distance of 24 km against the current and 36 km in direction of current, If it takes each time 6 hours then find the speed of current.

Answer : Speed of boat man upstream = 24/6 = 4 km/hr
Speed of boat man downstream = 36/6 = 6 km/hr
Speed of stream = 1/2(Speed of upstream + Speed of downstream) = 1/2(4 – 6)= 1km/hr.

Example 2: A boat running downstream and passes a distances of 16 km in 4 hours while covering the same distance upstream, takes 8 hours, Find the speed of the boat in still water ?

Answer : Rate of downstream = (16 / 4)kmph = 4 kmph
Rate of upstream = (16/8)kmph = 2kmph
Speed in still water = 1/2(4+2)kmph = 3kmph

Example 3:A boat covers in one hour about 12 km along with stream and 6 km against the stream. Then find the speed of boat in still water (in km/hr).

Answer : Speed of boat in still water = 1/2(12 + 6)kmph = 9 kmph.

Example 4: In one hour a boat covers 8 km against the stream and 12 km along the stream. What would be the speed of the boat in still water (in km/hr) ?

Answer : So, speed of boat in still water = U + V / 2 = (12 + 8 )/2 kmph = 10 kmph.

Example 5: A boat goes against the stream and covers 18 km in 3 hours while covering the same distance along the stream in 2 hours. What would be the speed of boat in still water ?

Answer : Rate of boat in upstream = (18 / 3)kmph = 6 kmph.
Rate of boat in downstream = (18 / 2) kmph = 9 kmph.
Speed of boat in still water = U + V / 2 = 9 + 6 / 2 = 7.5 kmph

Example 6: A boy can row upstream at 6 km/hr and downstream at 12 km/hr.find boy’s rate in still water and the rate of current ?

Answer : We Know the formula of Rate in still water that is = 1 / 2 ( x + y )km /hr
So we applied formula 1 / 2 ( 12 + 6 ) = 1 / 2 X 18 = 9 km/ hr. and
we also know the formula of
Rate of current that is = 1 / 2 ( x – y )km /hr
So we applied formula of 1 / 2 ( 12 – 6 ) = 3 km / hr.

Example 7: boy can row downstream at 24 km and upstream 16 km . If he takes 8 hours to cover each distance , then what is the velocity of the current ?

Answer : The rate of downstream = 24 / 8 km/hr ,
The rate of upstream = 16 / 8 km /hr .
So , the velocity of the current is 1 / 2 ( 24 / 8 – 16 / 8 ) km /hr = 1 / 2 km /hr.

Example 8: A man can go 40 km/hr upstream 36 km/hr downstream . Find the speed of current & speed of man in still water ?

Answer : Speed of current Y = U – V / 2
= 40 – 36 / 2 = 4 / 2
= 2 km/hr .
So , Speed of man in still water x is
= U + V / 2
= 40 + 36 / 2
= 38 km/hr

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