Vaidev started driving from City P towards City Q at 15 30 at an average speed of 60 km/h. Bryan began driving from City P towards City Q at 18 20 at an average speed of 110 km/h.

1. At what time did Bryan pass Vaidev on the road?
2. 1¹₁₀ hours after passing Vaidev, Bryan reached City Q. At what time did Vaidev reach City Q?

(a)
From 15 30 to 18 20 = 2 h 50 min

Time that Vaidev travelled before Bryan started driving = 2 h 50 min

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

Distance that Vaidev travelled before Bryan started driving
= 2⁵₆ x 60
= ¹⁷₆ x 60
= 170 km

Difference between Bryan's and Vaidev's speed
= 110 - 60
= 50 km/h

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

3 h 24 min after 18 20 = 21 44

Time that Bryan passed Vaidev on the road = 21 44

(b)
1¹₁₀ h = 1 h 6 min

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

4 h 30 min = 4³⁰₆₀h = 4¹₂h

Distance between City P and City Q
= 4¹₂ x 110
= 495 km

Time that Vaidev travelled from City P to City Q
= 495 ÷ 60
= 8.25 h
= 8 h 15 min

8 h 15 min after 15 30 = 23 45

Time that Vaidev reached City Q = 23 45

Answer: (a) 21 44; (b) 23 45