Xavier started driving from Village D towards Village E at 15 30 at an average speed of 60 km/h. Wesley began driving from Village D towards Village E at 17 10 at an average speed of 100 km/h.

1. At what time did Wesley pass Xavier on the road?
2. 1¹₄ hours after passing Xavier, Wesley reached Village E. At what time did Xavier reach Village E?

(a)
From 15 30 to 17 10 = 1 h 40 min

Time that Xavier travelled before Wesley started driving = 1 h 40 min

1 h = 60 min
1 h 40 min = 1⁴⁰₆₀ h = 1²₃ h

Distance that Xavier travelled before Wesley started driving
= 1²₃ x 60
= ⁵₃ x 60
= 100 km

Difference between Wesley's and Xavier's speed
= 100 - 60
= 40 km/h

Time that Wesley took to catch up with Xavier
= 100 ÷ 40
= 2.5 h
= 2 h 30 min

2 h 30 min after 17 10 = 19 40

Time that Wesley passed Xavier on the road = 19 40

(b)
1¹₄ h = 1 h 15 min

Total time that Wesley travelled
= 1 h 15 min + 2 h 30 min
= 3 h 45 min

3 h 45 min = 3⁴⁵₆₀h = 3³₄h

Distance between Village D and Village E
= 3³₄ x 100
= 375 km

Time that Xavier travelled from Village D to Village E
= 375 ÷ 60
= 6.25 h
= 6 h 15 min

6 h 15 min after 15 30 = 21 45

Time that Xavier reached Village E = 21 45

Answer: (a) 19 40; (b) 21 45