George started driving from City Q towards City R at 13 30 at an average speed of 60 km/h. Gabriel began driving from City Q towards City R at 17 20 at an average speed of 110 km/h.

1. At what time did Gabriel pass George on the road?
2. 1¹₁₀ hours after passing George, Gabriel reached City R. At what time did George reach City R?

(a)
From 13 30 to 17 20 = 3 h 50 min

Time that George travelled before Gabriel started driving = 3 h 50 min

1 h = 60 min
3 h 50 min = 3⁵⁰₆₀ h = 3⁵₆ h

Distance that George travelled before Gabriel started driving
= 3⁵₆ x 60
= ²³₆ x 60
= 230 km

Difference between Gabriel's and George's speed
= 110 - 60
= 50 km/h

Time that Gabriel took to catch up with George
= 230 ÷ 50
= 4.6 h
= 4 h 36 min

4 h 36 min after 17 20 = 21 56

Time that Gabriel passed George on the road = 21 56

(b)
1¹₁₀ h = 1 h 6 min

Total time that Gabriel travelled
= 1 h 6 min + 4 h 36 min
= 5 h 42 min

5 h 42 min = 5⁴²₆₀h = 5⁷₁₀h

Distance between City Q and City R
= 5⁷₁₀ x 110
= 627 km

Time that George travelled from City Q to City R
= 627 ÷ 60
= 10.45 h
= 10 h 27 min

10 h 27 min after 13 30 = 23 57

Time that George reached City R = 23 57

Answer: (a) 21 56; (b) 23 57