Zane started driving from Village A towards Village B at 15 30 at an average speed of 60 km/h. Archie began driving from Village A towards Village B at 17 20 at an average speed of 110 km/h.

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

(a)
From 15 30 to 17 20 = 1 h 50 min

Time that Zane travelled before Archie started driving = 1 h 50 min

1 h = 60 min
1 h 50 min = 1⁵⁰₆₀ h = 1⁵₆ h

Distance that Zane travelled before Archie started driving
= 1⁵₆ x 60
= ¹¹₆ x 60
= 110 km

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

Time that Archie took to catch up with Zane
= 110 ÷ 50
= 2.2 h
= 2 h 12 min

2 h 12 min after 17 20 = 19 32

Time that Archie passed Zane on the road = 19 32

(b)
1¹₁₀ h = 1 h 6 min

Total time that Archie travelled
= 1 h 6 min + 2 h 12 min
= 3 h 18 min

3 h 18 min = 3¹⁸₆₀h = 3³₁₀h

Distance between Village A and Village B
= 3³₁₀ x 110
= 363 km

Time that Zane travelled from Village A to Village B
= 363 ÷ 60
= 6.05 h
= 6 h 3 min

6 h 3 min after 15 30 = 21 33

Time that Zane reached Village B = 21 33

Answer: (a) 19 32; (b) 21 33