In a $500-\mathrm{m}$ race, $\mathrm{P}$ runs at $10 \mathrm{~m} / \mathrm{s}$. If $\mathrm{P}$ gives $\mathrm{Q}$ a start of $50 \mathrm{~m}$ and still wins the race by $5$ seconds, find the speed of $\text{Q}$.
- $8 \mathrm{~m} / \mathrm{s}$
- $8.18 \mathrm{~m} / \mathrm{s}$
- $9.01 \mathrm{~m} / \mathrm{s}$
- $9.19 \mathrm{~m} / \mathrm{s}$