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28 August, 21:56

A boat travels 12 km upstream and back in 1 hour 45 minutes. 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 significant figures.

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  1. 28 August, 21:59
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    14.3 km/h to 3 significant figures

    Step-by-step explanation:

    Let time travelling upstream be t1 hours and downstream = t2 hours.

    t1 + t2 = 1.75 ... (1)

    Let v be the speed of the boat in still water.

    12 / t1 = v - 3 ... (2)

    12 / t2 = v + 3 ... (3)

    From (1) and (3), substituting for t2:-

    12 / (1.75 - t1) = v + 3 ... (4)

    Subtract: - (2) - (4) : -

    12 / t1 - 12 / (1.75 - t1) = - 6

    12 (1.75 - t1) - 12t1 = - 6t1 (1.75 - t1)

    21 - 12t1 - 12t1 = - 10.5t1 + 6t^2

    6t1^2 + 13.5t1 - 21 = 0

    Solving this gives t1 = 1.058 hours

    Therefore the speed in still water (v) = 12/1.058 + 3 = 14.3 to 3 sig figs
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