Towns X, Y, and Z sit along a river with Y equidistant from X and Z. A boatman takes 10 hours for X to Y and back, and 4 hours for X to Z. Find the ratio of his still water speed to the current speed.
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Answer: B. 5:3
Explanation
Setting up algebraic equations for travel times between towns along a river establishes speed relationships. Comparing the boat speed in still water against the river current speed yields the required ratio. Simplifying the resulting fractional speed comparison determines a final ratio of five to three. River travel problems require accounting for both downstream and upstream velocity components. Still water speed represents the vessel velocity without any external water current interference. Ratio comparisons express the relative magnitude of two homogeneous physical quantities.
River navigation requires pilots to calculate vessel speed ratios to maintain accurate travel schedules. Hydraulic engineering studies fluid velocity profiles to optimize water transport efficiency. Physics problems involving relative motion build foundational mechanics problem solving skills. Option A suggests two to five which inverts the proper magnitude of the speed ratio. Option C proposes three to five which reverses the order of still water to current speeds. Option D offers one to two which lacks any valid derivation from the travel time equations.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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