(a)[2]
Calculate the average speed for the complete journey from $P$ to $Q$ to $R$, and then back from $R$ to $Q$ to $P$.
(b(i))[1]
Calculate the bearing from $Q$ to $R$.
(b(ii))[1]
Calculate the bearing from $Q$ to $P$.
Mathematics 4024 · O Level · Rates
Rates — practice question
A boat goes from $P$ to $Q$. On reaching $Q$, it turns through $90^{\circ}$ and continues to $R$ as the diagram shows. It then makes the return trip from $R$ to $Q$, and then back to $P$, retracing the same path in reverse. $PQ = 6\,\text{km}$ and $QR = 9\,\text{km}$. The outward part of the trip, from $P$ to $Q$ to $R$, lasts $3$ hours. The return leg, from $R$ to $Q$ to $P$, lasts $2$ hours.