Xavier started driving from Village R towards Village S at 15 45 at an average speed of 60 km/h. Julian began driving from Village R towards Village S at 17 35 at an average speed of 110 km/h.

1. At what time did Julian pass Xavier on the road?
2. 1¹₁₀ hours after passing Xavier, Julian reached Village S. At what time did Xavier reach Village S?

(a)
From 15 45 to 17 35 = 1 h 50 min

Time that Xavier travelled before Julian started driving = 1 h 50 min

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

Distance that Xavier travelled before Julian started driving
= 1⁵₆ x 60
= ¹¹₆ x 60
= 110 km

Difference between Julian's and Xavier's speed
= 110 - 60
= 50 km/h

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

2 h 12 min after 17 35 = 19 47

Time that Julian passed Xavier on the road = 19 47

(b)
1¹₁₀ h = 1 h 6 min

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

3 h 18 min = 3¹⁸₆₀h = 3³₁₀h

Distance between Village R and Village S
= 3³₁₀ x 110
= 363 km

Time that Xavier travelled from Village R to Village S
= 363 ÷ 60
= 6.05 h
= 6 h 3 min

6 h 3 min after 15 45 = 21 48

Time that Xavier reached Village S = 21 48

Answer: (a) 19 47; (b) 21 48