So this is what I've gotten so far

sin(theta) = 9/PQ so PQ = 9/sin(theta).

Call the point at the right angle S.

RS = sqrt(15^2 + 9^2) = sqrt(225 + 81) = sqrt(306) = 17.5

9/QS = tan(theta)

QS = 9/tan(theta)

QR = 17.5 - 9/tan(theta)

PQ = 9/sin(theta)

she travels 3km/h on PQ and 5 on QR. So it's PQ/3 + QR/5.

Is there a way to find out the lengths of PQ or QR or is what I have the answer?