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? |
8 km/h 5 km/h 6 km/h 4 km/h |
4 km/h |
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 |