A stream flows at 1 kmph. A motorboat travels 35 km upstream and returns in 12 hours. Find the boat's speed in still water_________?
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Answer: A. 6 kmph
Explanation
Letting the boat speed in still water be b, the upstream speed is b minus one and the downstream speed is b plus one. The total travel time equation is thirty-five divided by b minus one plus thirty-five divided by b plus one equals twelve hours. Solving this rational algebraic equation yields a valid boat speed of six kilometers per hour in still water. Upstream and downstream travel times are calculated by adjusting the boat's base speed by the speed of the river current. Rational equations resulting from distance-speed-time problems are solved by clearing denominators into standard quadratics. Checking potential solutions ensures the boat speed exceeds the stream current speed to allow upstream travel.
Option B results in a total travel time that fails to equal the specified twelve hours. Option C produces a fractional travel time that does not satisfy the balanced equation parameters. Option D yields an incorrect round-trip duration when tested against the one kmph stream current.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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