a motor boat whose speed is 18 km/ hour in still water takes 1 hour more to go 24 km upstream to the same spot . find the speed o

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1. Step-by-step explanation:

   Given parameters :-

   The speed of the motorboat in still water = 18 km/h

   Let as consider :–

   The speed of the stream = s

   Speed of boat upstream = Speed of a boat in still water – the speed of a stream

   Speed of boat upstream = 18 – s

   Speed of boat downstream = Speed of a boat in still water + speed of a stream

   Speed of boat downstream = 18 + s

   Time is taken for upstream = Time taken to cover downstream + 1

   [tex]\bold{time = \frac{distance}{speed} }[/tex]

   [tex]\implies \: \frac{Distance \: up \: stream}{Speed \: up \: stream} = \frac{Distance \: down \: stream}{Speed \: down \: stream} + 1[/tex]

   [tex]\implies\frac{24}{18 – s} = \frac{24}{18 + s} + 1[/tex]

   [tex]\implies \: \frac{24}{18 – s} = \frac{24 + (18 + s)}{18 + s}[/tex]

   [tex]\implies \scriptsize \: 24(18 + s) = (18 – s)[24 + (18 + s)][/tex]

   ⟹ 24(18+s) = 24(18−s) + (18−s)(18+s)

   ⟹ 432 + 24s = 432 – 24s + 18² – s²

   ⟹ 432 – 432 + 24s + 24s = 324 – s²

   ⟹ 48s = 324 – s²

   ⟹ s² + 48s − 324 = 0

   ⟹ s² + 54s − 6s − 324 = 0

   ⟹ (s + 54)(s − 6) = 0

   ⟹ s + 54 = 0 or s – 6 = 0

   ⟹ s = –54 or s = +6

   So, s = 6,−54

   but s ≠ −54

   Since the speed of steam cannot be negative.

   ∴ s = 6km/hr

   I hope it is helpful

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