Brandon started driving from Village N towards Village P at 15 40 at an average speed of 60 km/h. Luke began driving from Village N towards Village P at 17 20 at an average speed of 100 km/h.

1. At what time did Luke pass Brandon on the road?
2. 1¹₄ hours after passing Brandon, Luke reached Village P. At what time did Brandon reach Village P?

(a)
From 15 40 to 17 20 = 1 h 40 min

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

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

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

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

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

2 h 30 min after 17 20 = 19 50

Time that Luke passed Brandon on the road = 19 50

(b)
1¹₄ h = 1 h 15 min

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

3 h 45 min = 3⁴⁵₆₀h = 3³₄h

Distance between Village N and Village P
= 3³₄ x 100
= 375 km

Time that Brandon travelled from Village N to Village P
= 375 ÷ 60
= 6.25 h
= 6 h 15 min

6 h 15 min after 15 40 = 21 55

Time that Brandon reached Village P = 21 55

Answer: (a) 19 50; (b) 21 55