Answer:
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
