A Boat takes 128 min less to travel to 48 Km downstream than to travel the same distance upstream. If the speed of the stream is 3 Km/hr. Then Speed of Boat in still water is?a)12 Km/hrb)15 Km/hrc)6 Km/hrd)9 Km/hrCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

32/15 = 48(1/s-3 – 1/s+3)
s= 12
Therefore, Speed of Boat in still water is 12 Km/hr.

Answer

32/15 = 48(1/s-3 – 1/s+3)
s= 12
Therefore, Speed of Boat in still water is 12 Km/hr.

Answer

Understanding the Problem:
Let's assume the speed of the boat in still water is x Km/hr.
Speed downstream = (x + 3) Km/hr
Speed upstream = (x - 3) Km/hr
Time taken downstream = Distance / Speed = 48 / (x + 3)
Time taken upstream = Distance / Speed = 48 / (x - 3)

Formulating the Equation:
Given that the boat takes 128 min less time downstream compared to upstream:
48 / (x + 3) = 48 / (x - 3) + 128/60

Solving the Equation:
Solving the above equation, we get:
48 / (x + 3) = 48 / (x - 3) + 128/60
48(x - 3) = 48(x + 3) + 128(x^2 - 9)
48x - 144 = 48x + 144 + 128x^2 - 1152
128x^2 = 1152 + 144 + 144
128x^2 = 1440
x^2 = 1440 / 128
x^2 = 11.25
x = √11.25
x = 3.35 (approx)
Therefore, the speed of the boat in still water is approximately 3.35 Km/hr, which is closest to 3 Km/hr. Hence, the correct answer is option 'A' (12 Km/hr).

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