Question

A travels 60km downstream and 20km upstream in 4 hours.The same boat travels 40 km downstrean and 40km upstream in 6 hours.What is the speed of stream

Answer 1

Given:

A travels 60km downstream and 20km upstream in 4 hours.The same boat travels 40 km downstrean and 40km upstream in 6 hours.

To find:

Speed of stream

Calculation:

Let downstream Velocity of boat be u , upstream Velocity be v ;

1st case:

$\sf{ \dfrac{60}{u} + \dfrac{20}{v} = 4 \: \: \: \: ......(1)}$

2nd case:

$\sf{ \dfrac{40}{u} + \dfrac{40}{v} = 6 \: \: \: \: ......(2)}$

Putting 1/u = x and 1/v = y ;

$\sf{ 60x + 20y = 4 \: \: \: \: ......(3)}$

$\sf{ 40x + 40y = 6 \: \: \: \: ......(4)}$

After Solving eq. (3) and (4), we get:

$\sf{x = \dfrac{1}{40} \: and \:y = \dfrac{1}{8} }$

Now , replacing with u and v, we get;

$\sf{u = 40 \: km {hr}^{ - 1} \: and \: v = 8 \: km {hr}^{ - 1} }$

Let Velocity of boat be v_{b} and Velocity of stream be v_{s}

$\rm{u = v_{b} + v_{s} = 40}$

Again,

$\rm{v = v_{b} - v_{s} = 8}$

Subtracting the equations;

$\rm{ = > 2v_{s} = 32}$

$\rm{ = > v_{s} = 16 \: km {hr}^{ - 1} }$

So, final answer is:

$\boxed{ \rm{ velocity \: of \: stream = 16 \: km {hr}^{ - 1} }}$