Cole started driving from City Y towards City Z at 14 30 at an average speed of 60 km/h. Simon began driving from City Y towards City Z at 16 10 at an average speed of 100 km/h.

1. At what time did Simon pass Cole on the road?
2. 1¹₄ hours after passing Cole, Simon reached City Z. At what time did Cole reach City Z?

(a)
From 14 30 to 16 10 = 1 h 40 min

Time that Cole travelled before Simon started driving = 1 h 40 min

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

Distance that Cole travelled before Simon started driving
= 1²₃ x 60
= ⁵₃ x 60
= 100 km

Difference between Simon's and Cole's speed
= 100 - 60
= 40 km/h

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

2 h 30 min after 16 10 = 18 40

Time that Simon passed Cole on the road = 18 40

(b)
1¹₄ h = 1 h 15 min

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

3 h 45 min = 3⁴⁵₆₀h = 3³₄h

Distance between City Y and City Z
= 3³₄ x 100
= 375 km

Time that Cole travelled from City Y to City Z
= 375 ÷ 60
= 6.25 h
= 6 h 15 min

6 h 15 min after 14 30 = 20 45

Time that Cole reached City Z = 20 45

Answer: (a) 18 40; (b) 20 45