Paul started driving from Village Q towards Village R at 15 40 at an average speed of 60 km/h. Zeph began driving from Village Q towards Village R at 18 30 at an average speed of 110 km/h.

1. At what time did Zeph pass Paul on the road?
2. 1¹₁₀ hours after passing Paul, Zeph reached Village R. At what time did Paul reach Village R?

(a)
From 15 40 to 18 30 = 2 h 50 min

Time that Paul travelled before Zeph started driving = 2 h 50 min

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

Distance that Paul travelled before Zeph started driving
= 2⁵₆ x 60
= ¹⁷₆ x 60
= 170 km

Difference between Zeph's and Paul's speed
= 110 - 60
= 50 km/h

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

3 h 24 min after 18 30 = 21 54

Time that Zeph passed Paul on the road = 21 54

(b)
1¹₁₀ h = 1 h 6 min

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

4 h 30 min = 4³⁰₆₀h = 4¹₂h

Distance between Village Q and Village R
= 4¹₂ x 110
= 495 km

Time that Paul travelled from Village Q to Village R
= 495 ÷ 60
= 8.25 h
= 8 h 15 min

8 h 15 min after 15 40 = 23 55

Time that Paul reached Village R = 23 55

Answer: (a) 21 54; (b) 23 55