Valen started driving from Town N towards Town P at 13 40 at an average speed of 60 km/h. Lee began driving from Town N towards Town P at 16 30 at an average speed of 110 km/h.

1. At what time did Lee pass Valen on the road?
2. 1¹₁₀ hours after passing Valen, Lee reached Town P. At what time did Valen reach Town P?

(a)
From 13 40 to 16 30 = 2 h 50 min

Time that Valen travelled before Lee started driving = 2 h 50 min

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

Distance that Valen travelled before Lee started driving
= 2⁵₆ x 60
= ¹⁷₆ x 60
= 170 km

Difference between Lee's and Valen's speed
= 110 - 60
= 50 km/h

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

3 h 24 min after 16 30 = 19 54

Time that Lee passed Valen on the road = 19 54

(b)
1¹₁₀ h = 1 h 6 min

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

4 h 30 min = 4³⁰₆₀h = 4¹₂h

Distance between Town N and Town P
= 4¹₂ x 110
= 495 km

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

8 h 15 min after 13 40 = 21 55

Time that Valen reached Town P = 21 55

Answer: (a) 19 54; (b) 21 55