Xavier started driving from Town T towards Town U at 13 30 at an average speed of 60 km/h. Cody began driving from Town T towards Town U at 16 20 at an average speed of 110 km/h.

1. At what time did Cody pass Xavier on the road?
2. 1¹₁₀ hours after passing Xavier, Cody reached Town U. At what time did Xavier reach Town U?

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

Time that Xavier travelled before Cody started driving = 2 h 50 min

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

Distance that Xavier travelled before Cody started driving
= 2⁵₆ x 60
= ¹⁷₆ x 60
= 170 km

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

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

3 h 24 min after 16 20 = 19 44

Time that Cody passed Xavier on the road = 19 44

(b)
1¹₁₀ h = 1 h 6 min

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

4 h 30 min = 4³⁰₆₀h = 4¹₂h

Distance between Town T and Town U
= 4¹₂ x 110
= 495 km

Time that Xavier travelled from Town T to Town U
= 495 ÷ 60
= 8.25 h
= 8 h 15 min

8 h 15 min after 13 30 = 21 45

Time that Xavier reached Town U = 21 45

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