[tex]\huge{\underline{\underline{\bf Question}}}[/tex]

Speed of a Boat on still water is 15 km/hr. It goes 30 km upstr

2 thoughts on “[tex]\huge{\underline{\underline{\bf Question}}}[/tex] <br /><br />Speed of a Boat on still water is 15 km/hr. It goes 30 km upstr”

1. Given :

   • Speed of boat in water = 15 km/h
   • Distance travelled = 30km
   • Time taken = 4 hour 30 mins = [tex]\sf 4+\dfrac{1}{2}[/tex]

   To Find :

   • Speed of stream

   Solution :

   Let the Speed of stream be x

   Speed of stream in upstream = (15-x)

   Speed of stream in downstream = (15+x)

   Formula To Be used,

   [tex]\sf Speed = \dfrac{distance}{Time\:taken}\\\\\boxed{\boxed{\sf Time\:taken =\dfrac{distance}{Speed}}}[/tex]

   Given that,

   • Time taken = [tex]\sf 4+\dfrac{1}{2}\Rightarrow \dfrac{9}{2}[/tex]
   • Speed (Upstream) = (15 – x)
   • Speed (Downstream) = (15 + x)
   • Distance Travelled = 30 km

   Substituting values,

   [tex]\sf \rightarrow \dfrac{30}{(15+x)}+\dfrac{30}{(15-x)} =\dfrac{9}{2}\\\\\sf\rightarrow \dfrac{30(15-x)+30(15+x)}{(15+x)(15-x)}=\dfrac{9}{2}\\\\\sf \rightarrow\dfrac{450-{\cancel{30x}}+450+{\cancel{30x}}}{((15)^2-x^2)}\\\\\sf\rightarrow \dfrac{900}{(225-x^2)}=\dfrac{9}{2}\\\\\sf\rightarrow 2(900) = 9(225 – x^2)\\\\\sf \rightarrow1800 = 2025 -9x^2 \\\\\sf \rightarrow 1800 – 2025 = -9x^2\\\\\sf\rightarrow -9x^2 = -225\\\\\sf\rightarrow x^2 = \dfrac{-225}{-9}\\\\\sf\rightarrow x^2=25\\\\\sf \rightarrow x = \pm 5[/tex]

   Note :– Speed can not be negative

   Required Answer :

   Speed of the stream is [tex]\underline{\sf 5\:km/h}[/tex]

   Reply

2. [tex]\sf\underline \red{ Given}[/tex]

   • Speed of boat in water = 15 km/h
   • Distance travelled = 30km
   • Time taken = 4 hour 30 mins = [tex]\sf 4+\dfrac{1}{2}[/tex]

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

   • Speed of stream

   [tex]\sf\underline \pink{ Solution}[/tex]

   • Let the speed of the train be x km/h.
   • Downstream speed = (15 + x) km/h
   • Upstream speed = (15 – x) km/h

   • Time taken to go 30 km upstream = 30/(15 – x) hrs.
   • Time taken to go 30 km downstream = 30/(15 + x) hrs.

   According to the Question,

   • ⇒ 30/(15 – x) + 30/(15 + x) = 9/2
   • ⇒ 30(15 + x) + 30(15 – x)/(15 + x) (15 – x) = 9/2
   • ⇒ 450 + 30x + 450 – 30x/225 – x² = 9/2
   • ⇒ 900/225 – x² = 9/2

   By cross-multiplication, we get

   • ⇒ 9(225 – x²) = 1800
   • ⇒ 225 – x² = 200
   • ⇒ x² = 25
   • ⇒ x = ± 5

   (As speed can’t be negative)

   • ⇒ x = 5 km/h

   Hence, the speed of stream is 5 km/h.

   Reply