mathematics

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a boat travels 12 km upstream and back in 1 hour and 45 min.if the speed of the current is 3 km/h throughout,find the speed of the boat in still water,giving your answer correct to 3 decimal place.

NOTE:(Answer is 14.3 km/h,so can any one show me the solution).

  • mathematics -

    The speed in still water is X km/h, so the speed upstream is (X-3) km/h (slower than X because it's upstream), and the speed downstream is (X+3) km/h (faster than X because it's downstream).

    Travelling at (X-3) km/h for 12 km will take 12/(X-3) hours, and travelling back again at (X+3) km/h for 12 km will take another 12/(X+3) hours.

    But the whole journey takes 1.75 hours, so 12/(X-3) + 12/(X+3) = 1.75 = 7/4. We need to solve this for X. After a bit of algebraic shuffling of the above terms, we end up with 7X²-96X-63=0. One of the two solutions of this is negative and therefore impossible; the other one should be the answer you're looking for.

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