Problem:
A skiff leaves a dock and heads toward a house across the river. The house is at a bearing of $\mathrm{N}\,64^{\circ}\mathrm{E}$ from the dock. There is a $1$ mile per hour current blowing due east. Determine the speed and direction the skiff would have to maintain so that the skiff's actual speed is $4$ miles per hour and moving directly towards the house.
I know you can solve this with vectors and using trigonometry, but how would I do this?
Hint:
Firstly, the question asks that the skiff must move directly towards the house and for this to happen the current would need to be flowing due west, as this would then make sense as the westbound current will offset the eastward component of the skiff such that it travels in a straight line. So confirmation is needed on whether the direction of the current is due east or due west.
Otherwise we have: