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. F

1 thought on “The speed of the boat in stillwater is 18 Km/h. It can go 48 Km upstream and return to the<br /><br />original point in 6 hours. F”

1. [tex]\large\underline{\bold{Given- }}[/tex]

   • 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

   [tex]\large\underline{\sf{To\:Find – }}[/tex]

   • Speed of the stream

   [tex]\begin{gathered}\Large{\sf{{\underline{Formula \: Used – }}}} \end{gathered}[/tex]

   [tex] \: \: \: \: \: \: \: \: \: \: \: \boxed{ \bf{ \: Time \: = \: \dfrac{Distance}{Speed} }}[/tex]

   [tex]\large\underline{\sf{Solution-}}[/tex]

   • 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

   [tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: t_1 \: = \: \dfrac{48}{18 – x} \: hours[/tex]

   Case :- 2

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

   • Distance covered = 48 km

   So,

   • Time taken to covered 48 km in downstream is

   [tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: t_2 \: = \: \dfrac{48}{18 + x} [/tex]

   According to statement,

   • Total time taken = 6 hours

   [tex]\rm :\implies\:t_1 + t_2 = 6[/tex]

   [tex]\rm :\longmapsto\:\dfrac{48}{18 – x} + \dfrac{48}{18 + x} = 6[/tex]

   [tex]\rm :\longmapsto\:48\bigg(\dfrac{1}{18 – x} + \dfrac{1}{18 + x} \bigg) = 6[/tex]

   [tex]\rm :\longmapsto\:48\bigg(\dfrac{18 + x + 18 – x}{(18 + x)(18 – x)} \bigg) = 6[/tex]

   [tex]\rm :\longmapsto\:\dfrac{48 \times 36}{ {18}^{2} – {x}^{2} } = 6[/tex]

   [tex]\rm :\implies\:288 = 324 – {x}^{2} [/tex]

   [tex]\rm :\longmapsto\: {x}^{2} = 36[/tex]

   [tex]\rm :\implies\:x = 6 \: km \: per \: hour[/tex]

   [tex]\bf\implies \:Speed \: of \: stream \: is \: 6 \: km \: per \: hour[/tex]

   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

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