Zane started driving from Town H towards Town J at 14 30 at an average speed of 60 km/h. Riordan began driving from Town H towards Town J at 17 20 at an average speed of 110 km/h.

1. At what time did Riordan pass Zane on the road?
2. 1¹₁₀ hours after passing Zane, Riordan reached Town J. At what time did Zane reach Town J?

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

Time that Zane travelled before Riordan started driving = 2 h 50 min

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

Distance that Zane travelled before Riordan started driving
= 2⁵₆ x 60
= ¹⁷₆ x 60
= 170 km

Difference between Riordan's and Zane's speed
= 110 - 60
= 50 km/h

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

3 h 24 min after 17 20 = 20 44

Time that Riordan passed Zane on the road = 20 44

(b)
1¹₁₀ h = 1 h 6 min

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

4 h 30 min = 4³⁰₆₀h = 4¹₂h

Distance between Town H and Town J
= 4¹₂ x 110
= 495 km

Time that Zane travelled from Town H to Town J
= 495 ÷ 60
= 8.25 h
= 8 h 15 min

8 h 15 min after 14 30 = 22 45

Time that Zane reached Town J = 22 45

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