Asafa ran at a speed of $21 \mathrm{~km} / \mathrm{h}$ from $P$ to $Q$ to $R$ to $S$, as shown. Florence ran at a constant speed from $P$ directly to $R$ and then to $S$. They left $P$ at the same time and arrived at $S$ at the same time. How many minutes after Florence did Asafa arrive at point $R$ ?

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-100.jpg?height=246&width=477&top_left_y=2094&top_left_x=1190)
(A) 0
(B) 8
(C) 6
(D) 7
(E) 5
By the Pythagorean Theorem, $P R=\sqrt{Q R^{2}+P Q^{2}}=\sqrt{15^{2}+8^{2}}=\sqrt{289}=17 \mathrm{~km}$.

Asafa runs a total distance of $8+15+7=30 \mathrm{~km}$ at $21 \mathrm{~km} / \mathrm{h}$ in the same time that Florence runs a total distance of $17+7=24 \mathrm{~km}$.

Therefore, Asafa's speed is $\frac{30}{24}=\frac{5}{4}$ of Florence's speed, so Florence's speed is $\frac{4}{5} \times 21=\frac{84}{5} \mathrm{~km} / \mathrm{h}$.

Asafa runs the last $7 \mathrm{~km}$ in $\frac{7}{21}=\frac{1}{3}$ hour, or 20 minutes.

Florence runs the last $7 \mathrm{~km}$ in $\frac{7}{\frac{84}{5}}=\frac{35}{84}=\frac{5}{12}$ hour, or 25 minutes.

Since Asafa and Florence arrive at $S$ together, then Florence arrived at $R 5$ minutes before Asafa.

ANsWER: (E)