Question

The speed of the boat in stillwater is 18 Km/h. It can go 48 Km upstream and return to the

original point in 6 hours. Find the speed of the stream​

Answer 1

$\large\underline{\bold{Given- }}$

• Speed of boat in still water = 18 km/hr

• Distance covered in upstream = 48 km

• Distance covered in downstream = 48 km/hr

• Total time taken = 6 hours

$\large\underline{\sf{To\:Find - }}$

• Speed of the stream

$\begin{gathered}\Large{\sf{{\underline{Formula \: Used - }}}}  \end{gathered}$

$\: \: \: \: \: \: \: \: \: \: \: \boxed{ \bf{ \: Time \: = \: \dfrac{Distance}{Speed} }}$

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

• Let speed of the stream be 'x' km/hr.

Since,

• Speed of boat in still water = 18 km/hr

Therefore,

• Speed of upstream = (18 - x) km/hr

and

• Speed of downstream = (18 + x) km/hr

Now,

Case :- 1

• Speed of upstream = (18 - x) km/hr

• Distance covered = 48 km

So,

• Time taken to covered 48 km in upstream is

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: t_1 \: = \: \dfrac{48}{18 - x} \: hours$

Case :- 2

• Speed of downstream = (18 - x) km/hr

• Distance covered = 48 km

So,

• Time taken to covered 48 km in downstream is

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: t_2 \: = \: \dfrac{48}{18 + x}$

According to statement,

• Total time taken = 6 hours

$\rm :\implies\:t_1 + t_2 = 6$

$\rm :\longmapsto\:\dfrac{48}{18 - x} + \dfrac{48}{18 + x} = 6$

$\rm :\longmapsto\:48\bigg(\dfrac{1}{18 - x} + \dfrac{1}{18 + x} \bigg) = 6$

$\rm :\longmapsto\:48\bigg(\dfrac{18 + x + 18 - x}{(18 + x)(18 - x)} \bigg) = 6$

$\rm :\longmapsto\:\dfrac{48 \times 36}{ {18}^{2} - {x}^{2} } = 6$

$\rm :\implies\:288 = 324 - {x}^{2}$

$\rm :\longmapsto\: {x}^{2} = 36$

$\rm :\implies\:x = 6 \: km \: per \: hour$

$\bf\implies \:Speed \: of \: stream \: is \: 6 \: km \: per \: hour$

Basic Concept Used :-

1. Stream –

• The moving water in a river is called a stream.

2. Upstream –

• If the boat is flowing in the opposite direction to the stream, it is called upstream. In this case, the net speed of the boat is called the upstream speed.

• Speed of upstream = Speed of boat - Speed of stream

3. Downstream –

• If the boat is flowing along the direction of the stream, it is called downstream. In this case, the net speed of the boat is called the downstream speed.

• Speed of downstream = Speed of Boat- Speed of stream