Two places \( P \) and \( Q \) are at a distance 960 km from each other. Ahmed and Rami start walking from \( P \) to \( Q \) at 2 hours difference, where Ahmed leaves from \( P \) before Rami. Ahmed and Rami both have \( 60 \mathrm{~km} / \mathrm{h} \) and \( 80 \mathrm{~km} / \mathrm{h} \) speed resepectively. Rami goes ahead of Ahmed at point \( M \), which falls somewhere between \( P \) and \( Q \), then how long will it take for Rami to get ahead of ahmed?

To find out how long it takes for Rami to get ahead of Ahmed, we can first establish some key points. Ahmed starts walking earlier than Rami, specifically 2 hours earlier, and his speed is 60 km/h. In those 2 hours, he would have covered: \[ \text{Distance travelled by Ahmed} = \text{Speed} \times \text{Time} = 60 \text{ km/h} \times 2 \text{ h} = 120 \text{ km} \] When Rami starts walking, Ahmed is already 120 km ahead. Rami walks at a speed of 80 km/h, while Ahmed walks at 60 km/h. The relative speed between Rami and Ahmed is: \[ 80 \text{ km/h} - 60 \text{ km/h} = 20 \text{ km/h} \] Now, we can calculate how long it will take for Rami to make up that 120 km difference at a relative speed of 20 km/h: \[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{120 \text{ km}}{20 \text{ km/h}} = 6 \text{ hours} \] So, it will take Rami 6 hours to catch up to Ahmed after he starts walking. Ahmed and Rami's journey highlights the different speeds at which they travel and how a head start can impact a chase! Life is like a race; sometimes those who start earlier need to keep up with the speedsters! Whether you're on foot or just trying to achieve your goals, sometimes you have to strategize to gain the advantage. Good luck, and may you run your best race!