Numerical answer
A boat's speed in still water is 15 km/h and the speed of the current is 5 km/h. The boat goes from point A to point B downstream and returns from B to A upstream, taking a total of 4.5 hours. Find the distance between A and B (in km).
Show answer and solution
Answer: 30
Downstream speed = 15+5 = 20 km/h, upstream speed = 15−5 = 10 km/h. If the one-way distance is d, total time = d/20 + d/10 = d(1/20+2/20) = 3d/20. Setting 3d/20 = 4.5 gives d = 4.5×20/3 = 30 km. Shortcut: total time for a round trip = 2d×b/(b²−c²) where b, c are boat and current speeds — here 2d×15/(225−25) = 30d/200 = 3d/20, matching the direct method.
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