Fabian started driving from City Y towards City Z at 13 40 at an average speed of 60 km/h. Ahmad began driving from City Y towards City Z at 15 20 at an average speed of 100 km/h.

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

(a)
From 13 40 to 15 20 = 1 h 40 min

Time that Fabian travelled before Ahmad started driving = 1 h 40 min

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

Distance that Fabian travelled before Ahmad started driving
= 1²₃ x 60
= ⁵₃ x 60
= 100 km

Difference between Ahmad's and Fabian's speed
= 100 - 60
= 40 km/h

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

2 h 30 min after 15 20 = 17 50

Time that Ahmad passed Fabian on the road = 17 50

(b)
1¹₄ h = 1 h 15 min

Total time that Ahmad 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 Fabian travelled from City Y to City Z
= 375 ÷ 60
= 6.25 h
= 6 h 15 min

6 h 15 min after 13 40 = 19 55

Time that Fabian reached City Z = 19 55

Answer: (a) 17 50; (b) 19 55