Sean started driving from Village C towards Village D at 13 45 at an average speed of 60 km/h. Ken began driving from Village C towards Village D at 15 35 at an average speed of 110 km/h.

1. At what time did Ken pass Sean on the road?
2. 1¹₁₀ hours after passing Sean, Ken reached Village D. At what time did Sean reach Village D?

(a)
From 13 45 to 15 35 = 1 h 50 min

Time that Sean travelled before Ken started driving = 1 h 50 min

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

Distance that Sean travelled before Ken started driving
= 1⁵₆ x 60
= ¹¹₆ x 60
= 110 km

Difference between Ken's and Sean's speed
= 110 - 60
= 50 km/h

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

2 h 12 min after 15 35 = 17 47

Time that Ken passed Sean on the road = 17 47

(b)
1¹₁₀ h = 1 h 6 min

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

3 h 18 min = 3¹⁸₆₀h = 3³₁₀h

Distance between Village C and Village D
= 3³₁₀ x 110
= 363 km

Time that Sean travelled from Village C to Village D
= 363 ÷ 60
= 6.05 h
= 6 h 3 min

6 h 3 min after 13 45 = 19 48

Time that Sean reached Village D = 19 48

Answer: (a) 17 47; (b) 19 48