Question

A boat takes $6$ hours to travel $8km$ upstream and $32km$ downstream and it takes $7$ hours to travel $20km$ upstream and $16km$ downstream. Find the speed of the boat in still water and the speed of the stream.

• A. $6,2$
• B. $6,1$
• C. $6,7$
• D. $6,9$

Answer 1

The correct option is A $6,2$

Let the speed of the boat in still water be $x$ km/hr

Let the speed of the stream be $y$ km/hr

The speed of the boat downstream $=$ $(x+y)$ km/hr

The speed of the boat upstream $=$ $(x-y)$ km/hr

$Time=\frac{Distance}{Speed}$

$6$ hours to travel $8$ km upstream and $32$ km downstream,

i. e $6=\frac{8}{x-y}+\frac{32}{x+y}$ (1)

$7$ hours to travel $20$ km upstream and $16$ km downstream.

i.e $7=\frac{20}{x-y}+\frac{16}{x+y}$ (2)

Let $\frac{1}{x-y}=a$ and $\frac{1}{x+y}=b$

$\therefore 6=8a+32b$ ...(3)

$7=20a+16b$ ...(4)

On solving the equations, we get $a=\frac{1}{4}$ and $b=\frac{1}{8}$

$\frac{1}{x-y}=\frac{1}{4}$ and $\frac{1}{x+y}=\frac{1}{8}$

$⟹4=x-y$

$⟹8=x+y$

Add the above (2) eqn we get

$12=2xx=6$ and $y=2$

So, the speed of the boat in still water $=$ $6$ km/hr

The speed of the stream $=$ $2$ km/hr