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.

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