Question

the speed of a boat in still water is 18 km/hr.It can go 48km upstream and return to the original point in 6 hours find the speed of the stream..please write correct answer​

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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