Fabian started driving from City D towards City E at 15 30 at an average speed of 60 km/h. Luke began driving from City D towards City E at 17 20 at an average speed of 110 km/h.

1. At what time did Luke pass Fabian on the road?
2. 1¹₁₀ hours after passing Fabian, Luke reached City E. At what time did Fabian reach City E?

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

Time that Fabian travelled before Luke started driving = 1 h 50 min

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

Distance that Fabian travelled before Luke started driving
= 1⁵₆ x 60
= ¹¹₆ x 60
= 110 km

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

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

2 h 12 min after 17 20 = 19 32

Time that Luke passed Fabian on the road = 19 32

(b)
1¹₁₀ h = 1 h 6 min

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

3 h 18 min = 3¹⁸₆₀h = 3³₁₀h

Distance between City D and City E
= 3³₁₀ x 110
= 363 km

Time that Fabian travelled from City D to City E
= 363 ÷ 60
= 6.05 h
= 6 h 3 min

6 h 3 min after 15 30 = 21 33

Time that Fabian reached City E = 21 33

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