Question

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 of steam​

Answer 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

$\bold{time = \frac{distance}{speed} }$

$\implies \: \frac{Distance \: up \: stream}{Speed \: up \: stream} = \frac{Distance \: down \: stream}{Speed \: down \: stream} + 1$

$\implies\frac{24}{18 - s} = \frac{24}{18 + s} + 1$

$\implies \: \frac{24}{18 - s} = \frac{24 + (18 + s)}{18 + s}$

$\implies \scriptsize \: 24(18 + s) = (18 - s)[24 + (18 + s)]$

⟹ 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