1. **State the problem:** Jason plans to complete a journey in 1.5 hours (which is 90 minutes). He drives at an average speed of 48 km/h and takes 50 minutes to complete half of his journey. We need to find by how many km/h his average speed must be increased to complete the journey in time. 2. **Given:** - Total time planned: $1.5$ hours = $90$ minutes - Speed for first half: $48$ km/h - Time for first half: $50$ minutes 3. **Find the distance of half the journey:** Since speed = distance / time, distance = speed \times time. Convert 50 minutes to hours: $\frac{50}{60} = \frac{5}{6}$ hours. Distance for half journey = $48 \times \frac{5}{6} = 48 \times 0.8333 = 40$ km. 4. **Total distance:** Since 40 km is half the journey, total distance = $2 \times 40 = 80$ km. 5. **Time left for second half:** Total time planned = 90 minutes, time used = 50 minutes, so time left = $90 - 50 = 40$ minutes = $\frac{2}{3}$ hours. 6. **Find required speed for second half to finish on time:** Speed = distance / time = $40 \div \frac{2}{3} = 40 \times \frac{3}{2} = 60$ km/h. 7. **Calculate increase in speed:** Increase = required speed - original speed = $60 - 48 = 12$ km/h. **Final answer:** Jason must increase his average speed by **12 km/h** to complete the journey in time.