Tim started driving from Town C towards Town D at 14 30 at an average speed of 60 km/h. Ken began driving from Town C towards Town D at 17 20 at an average speed of 110 km/h.

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

(a)
From 14 30 to 17 20 = 2 h 50 min

Time that Tim travelled before Ken started driving = 2 h 50 min

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

Distance that Tim travelled before Ken started driving
= 2⁵₆ x 60
= ¹⁷₆ x 60
= 170 km

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

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

3 h 24 min after 17 20 = 20 44

Time that Ken passed Tim on the road = 20 44

(b)
1¹₁₀ h = 1 h 6 min

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

4 h 30 min = 4³⁰₆₀h = 4¹₂h

Distance between Town C and Town D
= 4¹₂ x 110
= 495 km

Time that Tim travelled from Town C to Town D
= 495 ÷ 60
= 8.25 h
= 8 h 15 min

8 h 15 min after 14 30 = 22 45

Time that Tim reached Town D = 22 45

Answer: (a) 20 44; (b) 22 45