A drifting boat

Very happy to solve this awsome problem,

Since the resultant velocity is always perpendicular to the line joining the boat and $R$ , the boat is moving in a circle of radius $2w$ .

1) Thus the drift will be $QS$ = $\sqrt{4w^2 - w^2}$ = $\sqrt{3}w$

2) Suppose at any arbitrary time, the boat is at point $B$ .

$V_{net}$ = $2v\cos\theta$

$\dfrac {d \theta}{dt}$ = $\dfrac{V_{net}}{2w}$ = $\dfrac{v\cos\theta}{w}$

Cross multiplying :-

$\dfrac{w}{v}\sec\theta d\theta$ = $dt$

Now integrating and using proper limits(at time $t = 0$ , the line joining R and P makes an angle of $0^\circ$ , and at time $t$ , the angle becomes $60^\circ$ )

$\displaystyle\int^t_0d\theta$ = $\dfrac{w}{v}\displaystyle\int^{60^\circ}_0 \sec\theta d\theta$

$t$ = $\dfrac{w}{v}[ln(\sec\theta + \tan\theta)]^{60^\circ}_0$

$t$ = $\dfrac{1.317w}{v}$

So adding them we get :-

$[(1.317)(10) + \sqrt{3}](100)$

= $\boxed{186.375}$

P.S If someone could pls help me with this solution by providing an image, it would be really great as it may prove to be difficult to deduce what angle is $\theta$ and some of the other things too.