Archie started driving from City K towards City L at 14 40 at an average speed of 60 km/h. Justin began driving from City K towards City L at 17 30 at an average speed of 110 km/h.

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

(a)
From 14 40 to 17 30 = 2 h 50 min

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

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

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

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

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

3 h 24 min after 17 30 = 20 54

Time that Justin passed Archie on the road = 20 54

(b)
1¹₁₀ h = 1 h 6 min

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

4 h 30 min = 4³⁰₆₀h = 4¹₂h

Distance between City K and City L
= 4¹₂ x 110
= 495 km

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

8 h 15 min after 14 40 = 22 55

Time that Archie reached City L = 22 55

Answer: (a) 20 54; (b) 22 55