Question
A boat can travel 50 km upstream in 5 hours and 60 km
downstream in 4 hours. Find the speed of the boat in still water.Solution
Let the speed of the boat in still water be x km/h and the speed of the stream be y km/h. Upstream speed = (x - y) km/h, Downstream speed = (x + y) km/h. Time taken to travel upstream = 50 ÷ (x - y) = 5 hours. Time taken to travel downstream = 60 ÷ (x + y) = 4 hours. From the first equation: 50 ÷ (x - y) = 5 ⇒ (x - y) = 10 km/h. From the second equation: 60 ÷ (x + y) = 4 ⇒ (x + y) = 15 km/h. Solving the two equations: x - y = 10 x + y = 15 Adding both equations: 2x = 25 ⇒ x = 12.5 km/h. Correct Option: b) 12.5 km/h
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