Question

A boat goes same distance in upstream in 6 hour and the cover the same distance in the downward in the 4 hour .If the speed of the stream is 3 kilometre per hour then the distance is

Answer 1

Given :

Speed of stream = 3km/hr

upstream time = 6hrs

downstream time = 4hrs

Let the distance between the two parts be x km

Down speed stream =x/4 km/hr

upstream speed = x/6 km/hr

speed of stream

= 1/2(x/4 - x/6)

= 1/2(3x - 2x)/12

= x/24

Speed of stream

= x/24

= 3x

= 72km

∴ Distance is 72km

Some other Formulas :

• Speed = d/t

• F = m. a

• a (bar) = v - v_0/t = Δv/Δt

• w = F x d

• P = W/Δt

• V = 1R

• PE = mgh

• p = mv

Answer 2

$\huge\bf{\underbrace{\gray{GIVEN:-}}}$

• A boat goes same distance towards upstream in 6 hrs. .

• And covered the same distance towards downstream in 4 hrs. .

• The speed of the stream is 3 km/hr .

$\huge\bf{\underbrace{\gray{TO\:FIND:-}}}$

• The total distance covered by boat .

$\huge\bf{\underbrace{\gray{SOLUTION:-}}}$

Let,

• $\bf\red{Total\:distance}$ = X m

• $\bf\red{Speed\:of\:boat}$ = U km/hr .

Speed towards upstream :-

• Speed of boat - Speed of stream

$\bf\pink{:\implies\:(U\:-\:3)\:km/hr\:}$

Speed towards downstream :-

• Speed of boat + Speed of stream

$\bf\pink{:\implies\:(U\:+\:3)\:km/hr\:}$

Time towards upstream :-

$\huge\red\checkmark$ $\bf\purple{Time\:=\:\dfrac{X}{U\:-\:3}\:hrs\:}$

$\rm{:\implies\:6\:=\:\:\dfrac{X}{U\:-\:3}\:}$

$\bf{:\implies\:X\:=\:(U\:-\:3)\times{6}\:}$ ----(1)

Time towards downstream :-

$\huge\red\checkmark$ $\bf\purple{Time\:=\:\dfrac{X}{U\:+\:3}\:hrs\:}$

$\rm{:\implies\:4\:=\:\:\dfrac{X}{U\:+\:3}\:}$

$\bf{:\implies\:X\:=\:(U\:+\:3)\times{4}\:}$ ----(2)

☞︎︎︎ It is given that,

• The boat goes same distance both towards upstream and downstream .

$\bf\blue{:\implies\:\:(U\:-\:3)\times{6}\:=\:\:(U\:+\:3)\times{4}\:}$

➳ 6U - 18 = 4U + 12

➳ 6U - 4U = 12 + 18

➳ 2U = 30

➳ U = 30/3

➳ U = 15 km/hr

$\huge\therefore$ Speed of the boat is "15 km/hr" .

☯︎ Now, we can find the distance either from equation (1) or from the equation (2) . So, now we can put the value in equation (1),

$\blue\bigstar\:\bf\orange{Distance\:(X)\:=\:(U\:-\:3)\times{6}\:}$

$\rm{:\implies\:Distance\:(X)\:=\:(15\:-\:3)\times{6}\:}$

$\rm{:\implies\:Distance\:(X)\:=\:12\times{6}\:}$

$\bf\green{:\implies\:Distance\:(X)\:=\:72\:km\:}$

$\huge\red\therefore$ The total distance is "72 km" .