Question

speed of boat in still water is 15 km /h . it goes 30 km upstream and return back at the same point in 4 hours 30 minutes. find the speed of the stream

Answer 1

Answer:

Step-by-step explanation:

The speed of the boat in still water is 15km/hr.It can go 30 km upstream and return to down stream in 41/2hrs.find the speed of the stream.

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let x=speed of stream

(15+x)=speed of boat downstream

(15-x)=speed of boat upstream

travel time=distance/speed

30/(15+x)+30/(15-x)=9/2

60/(15+x)+60/(15-x)=9

LCD: (15+x)(15-x)

60(15-x)+60(15+x)=9(15+x)(15-x)

60(15-x+15+x)=9(225-x^2)

60(30)=2025-9x2

9x^2=2025-1800

9x2=225

take sqrt of both sides

3x=15

x=5

speed of stream=5 km/hr

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the of the stream be x km/h.

Time taken to cover 30 km upstream = 30/15 - x

Time taken to cover 30 km downstream = 30/15 + x

According to the Question,

⇒ 30/(15 - x) + 30/(15 + x) = 9/2

⇒ 30[(15 - x) + (15 - x)/(15 - x)(15 + x)] = 9/2

⇒ 30[30/225 - x²] = 9/2

⇒ 225 - x² = 200

⇒ x² = 225 - 200

⇒ x² = 25

⇒ x = - 5, 5 (As speed can't be negative)

⇒ x = 5

Speed of stream = x = 5 km/h.

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