Directions: These questions are based on the following information: $P$ and $Q$ are $120$ km apart. $A$ starts from $P$ towards $Q$ at 6 a.m. $B$ starts from $Q$ towards $P$ at 11 a.m. on the same day. $A$ is $50$ % faster than $B$. They cross each other at 8 p.m. In reaching his destination, how many more hours than $A$, will $B$ take?

### Concept & Total Journey Time Once individual speeds are determined using distance proportionality from the meeting point, the total time for each person to complete the full journey is simply the total distance divided by their respective speeds. ### Step-by-Step Solution * **Given:** Total distance = $120$ km. $A$ travels $14$ hours and $B$ travels $9$ hours until meeting. $A$'s speed is $1.5$ times $B$'s speed. * **Calculation:** From earlier derivations, $A$'s speed is $6$ km/hr and $B$'s speed is $4$ km/hr. * Total time taken by $A$ to travel the entire $120$ km = $\frac{120}{6} = 20$ hours. * Total time taken by $B$ to travel the entire $120$ km = $\frac{120}{4} = 30$ hours. * The question asks for the difference in their total travel times to reach their respective destinations. * Time difference = $30 - 20 = 10$ hours. ### Exam Strategy & Shortcut Since you already know $A$ takes $20$ hours and $B$ travels at $\frac{2}{3}$ the speed of $A$, it stands to reason that $B$ will take $\frac{3}{2}$ the time of $A$. So, $B$ takes $1.5 \times 20 = 30$ hours. The difference is $30 - 20 = 10$ hours, avoiding the need to fully calculate $B$'s speed. ### Common Pitfall Misreading the question and answering with the time difference it took them just to meet (which is $14 - 9 = 5$ hours) instead of the time difference to complete the entire destination journey. ### Final Answer Therefore, the correct answer is **$10$**.