Riordan started driving from Village A towards Village B at 15 30 at an average speed of 60 km/h. Luke began driving from Village A towards Village B at 18 20 at an average speed of 110 km/h.

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

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

Time that Riordan travelled before Luke started driving = 2 h 50 min

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

Distance that Riordan travelled before Luke started driving
= 2⁵₆ x 60
= ¹⁷₆ x 60
= 170 km

Difference between Luke's and Riordan's speed
= 110 - 60
= 50 km/h

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

3 h 24 min after 18 20 = 21 44

Time that Luke passed Riordan on the road = 21 44

(b)
1¹₁₀ h = 1 h 6 min

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

4 h 30 min = 4³⁰₆₀h = 4¹₂h

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

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

8 h 15 min after 15 30 = 23 45

Time that Riordan reached Village B = 23 45

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