Archie started driving from City A towards City B at 15 30 at an average speed of 60 km/h. David began driving from City A towards City B at 18 20 at an average speed of 110 km/h.

1. At what time did David pass Archie on the road?
2. 1¹₁₀ hours after passing Archie, David reached City B. At what time did Archie reach City B?

(a)
From 15 30 to 18 20 = 2 h 50 min

Time that Archie travelled before David started driving = 2 h 50 min

1 h = 60 min
2 h 50 min = 2⁵⁰₆₀ h = 2⁵₆ h

Distance that Archie travelled before David started driving
= 2⁵₆ x 60
= ¹⁷₆ x 60
= 170 km

Difference between David's and Archie's speed
= 110 - 60
= 50 km/h

Time that David took to catch up with Archie
= 170 ÷ 50
= 3.4 h
= 3 h 24 min

3 h 24 min after 18 20 = 21 44

Time that David passed Archie on the road = 21 44

(b)
1¹₁₀ h = 1 h 6 min

Total time that David travelled
= 1 h 6 min + 3 h 24 min
= 4 h 30 min

4 h 30 min = 4³⁰₆₀h = 4¹₂h

Distance between City A and City B
= 4¹₂ x 110
= 495 km

Time that Archie travelled from City A to City B
= 495 ÷ 60
= 8.25 h
= 8 h 15 min

8 h 15 min after 15 30 = 23 45

Time that Archie reached City B = 23 45

Answer: (a) 21 44; (b) 23 45