Question

$\huge{\underline{\underline{\bf Question}}}$

Speed of a Boat on still water is 15 km/hr. It goes 30 km upstream and returns back at the same point 4 hours 30 minutes. Find the speed of the stream

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Step by step explanation ✅

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Answer 1

Given :

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

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,

$\sf Speed = \dfrac{distance}{Time\:taken}\\\\\boxed{\boxed{\sf Time\:taken =\dfrac{distance}{Speed}}}$

Given that,

• Time taken = $\sf 4+\dfrac{1}{2}\Rightarrow \dfrac{9}{2}$
• Speed (Upstream) = (15 - x)
• Speed (Downstream) = (15 + x)
• Distance Travelled = 30 km

Substituting values,

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

Note :- Speed can not be negative

Required Answer :

Speed of the stream is $\underline{\sf 5\:km/h}$

Answer 2

$\sf\underline \red{ Given}$

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

$\sf\underline \gray{ To\:Find}$

• Speed of stream

$\sf\underline \pink{ Solution}$

• 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.