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?