Tim started driving from Town G towards Town H at 13 40 at an average speed of 60 km/h. Brandon began driving from Town G towards Town H at 15 20 at an average speed of 100 km/h.

1. At what time did Brandon pass Tim on the road?
2. 1¹₄ hours after passing Tim, Brandon reached Town H. At what time did Tim reach Town H?

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

Time that Tim travelled before Brandon started driving = 1 h 40 min

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

Distance that Tim travelled before Brandon started driving
= 1²₃ x 60
= ⁵₃ x 60
= 100 km

Difference between Brandon's and Tim's speed
= 100 - 60
= 40 km/h

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

2 h 30 min after 15 20 = 17 50

Time that Brandon passed Tim on the road = 17 50

(b)
1¹₄ h = 1 h 15 min

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

3 h 45 min = 3⁴⁵₆₀h = 3³₄h

Distance between Town G and Town H
= 3³₄ x 100
= 375 km

Time that Tim travelled from Town G to Town H
= 375 ÷ 60
= 6.25 h
= 6 h 15 min

6 h 15 min after 13 40 = 19 55

Time that Tim reached Town H = 19 55

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