A stream current flows at 4 kmph. A boat travels 6 km and returns in 2 hours; find the boat's speed in still water.
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Answer: C. 8 kmph
Explanation
Letting the boat speed in still water be b, the upstream speed is b minus four and the downstream speed is b plus four. The total travel time equation is six divided by b minus four plus six divided by b plus four equals two hours. Solving this rational algebraic equation yields a valid boat speed of eight kilometers per hour in still water. Stream current problems involve relative speed where current adds to boat speed downstream and subtracts upstream. Time equals distance divided by relative speed for both legs of a round-trip journey in moving water. Rational equations are solved by finding common denominators and reducing the resulting quadratic expression.
Option A results in an incorrect total travel time when substituted back into the upstream and downstream formula. Option B overestimates the boat speed, yielding a travel time shorter than the specified two hours. Option D fails to satisfy the round-trip time equation when tested against the four kmph current.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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