Question

A motor bike takes 2 hours to travel a distance of 9km down the current,and it takes 6 hours to travel the same distance against the current,the speed of the boat in still water and that of the current, are respectively?​

Answer 1

Appropriate Question :-

A boat takes 2 hours to travel a distance of 9km down the current, and it takes 6 hours to travel the same distance against the current. The speed of the boat in still water and that of the current, are respectively?

$\large\underline{\bf{Solution-}}$

Let speed of boat in still water = x km/hr

Let speed of current = y km/hr

So,

• Speed of upstream = x - y km/hr

• Speed of downstream = x + y km/hr

Case :- 1

Distance covered in downstream = 9 km

Time taken to cover 9 km = 2 hours

Speed of downstream = x + y km/hr

We know that,

Distance = Speed × Time

$\rm :\longmapsto\:9 = 2(x + y)$

$\rm :\longmapsto\:9 = 2x + 2y - - - (1)$

Case :- 2

Distance covered in upstream = 9 km

Time taken to cover 9 km = 6 hours

Speed of upstream = x - y km/hr

We know that,

Distance = Speed × Time

$\rm :\longmapsto\:9 = 6(x - y)$

$\rm :\longmapsto\:9 = 6x - 6y$

$\rm :\longmapsto\:3 = 2x - 2y - - - (2)$

On adding equation (1) and equation (2), we get

$\rm :\longmapsto\:3 + 9 = 2x - 2y + 2x + 2y$

$\rm :\longmapsto\:12 = 4x$

$\bf\implies \:x = 3$

Put x = 3 in equation (2), we get

$\rm :\longmapsto\:2 = 3 - y$

$\rm :\longmapsto\:2 - 3 = - y$

$\rm :\longmapsto\:- 1 = - y$

$\bf\implies \:y = 1$

$\begin{gathered}\begin{gathered}\bf\: Hence-\begin{cases} &\sf{Speed \: of \: boat \: in \: still \: water = 3 \: km \: per \: hr} \\ &\sf{Speed \: of \: current = 1 \: km \: per \: hr} \end{cases}\end{gathered}\end{gathered}$