Luke started driving from Town P towards Town Q at 13 30 at an average speed of 60 km/h. Ken began driving from Town P towards Town Q at 16 20 at an average speed of 110 km/h.

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

(a)
From 13 30 to 16 20 = 2 h 50 min

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

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

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

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

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

3 h 24 min after 16 20 = 19 44

Time that Ken passed Luke on the road = 19 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 P and Town Q
= 4¹₂ x 110
= 495 km

Time that Luke travelled from Town P to Town Q
= 495 ÷ 60
= 8.25 h
= 8 h 15 min

8 h 15 min after 13 30 = 21 45

Time that Luke reached Town Q = 21 45

Answer: (a) 19 44; (b) 21 45