A boat running upstream takes 12 hours 36 minutes to cover a certain distance, while it takes 4 hours 12 minutes to cover the same distance running downstream. What is the ratio between the speed of the boat in still water and speed of the current, respectively?
2 : 1
For a fixed distance, speed is inversely proportional to time. Upstream speed = b – c and downstream speed = b + c, where b is the speed in still water and c the speed of the current.
Times: 12 h 36 min = 12.6 h and 4 h 12 min = 4.2 h, so upstream : downstream speed = 4.2 : 12.6 = 1 : 3.
Let b – c = x and b + c = 3x. Adding, 2b = 4x so b = 2x; subtracting, 2c = 2x so c = x.
Therefore b : c = 2x : x = 2 : 1.
Check: take b = 2 and c = 1 (in some unit); upstream speed 1 and downstream speed 3 give times in the ratio 3 : 1, and 12.6 : 4.2 = 3 : 1.
Hence, 2 : 1.
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