A boat goes 8 km upstream and returns. If speed of the current is 1 km/h and the total time taken to cover to and for distance is 4 hours 16 minutes, then what is the speed of the boat in still water?
Answer & explanation
Correct answer: option 4
Distance = Speed × Time
Let us consider that Speed of boat is = S km/h
Downstream speed = ( S + 1 ) km/h
Downstream speed = ( S - 1 ) km/h
According to question,
\(\frac{8}{S + 1 }\) + \(\frac{8}{S - 1 }\) = 4 hours 16 minutes
\(\frac{8}{S + 1 }\) + \(\frac{8}{S - 1 }\) = \(\frac{64}{15 }\)
\(\frac{1}{S + 1 }\) + \(\frac{1}{S - 1 }\) = \(\frac{8}{15 }\)
\(\frac{2S}{S² - 1 }\) = \(\frac{8}{15 }\)
\(\frac{S}{S² - 1 }\) = \(\frac{4}{15 }\)
15S = 4 ( S² - 1 )
4S² - 15S - 4 = 0
4S² - 16S + S - 4 = 0
By solving ,
S = 4 km/h
The correct answer is Option (4) → 4 km/h