Brandon started driving from Village S towards Village T at 15 40 at an average speed of 60 km/h. Billy began driving from Village S towards Village T at 17 30 at an average speed of 110 km/h.

1. At what time did Billy pass Brandon on the road?
2. 1¹₁₀ hours after passing Brandon, Billy reached Village T. At what time did Brandon reach Village T?

(a)
From 15 40 to 17 30 = 1 h 50 min

Time that Brandon travelled before Billy started driving = 1 h 50 min

1 h = 60 min
1 h 50 min = 1⁵⁰₆₀ h = 1⁵₆ h

Distance that Brandon travelled before Billy started driving
= 1⁵₆ x 60
= ¹¹₆ x 60
= 110 km

Difference between Billy's and Brandon's speed
= 110 - 60
= 50 km/h

Time that Billy took to catch up with Brandon
= 110 ÷ 50
= 2.2 h
= 2 h 12 min

2 h 12 min after 17 30 = 19 42

Time that Billy passed Brandon on the road = 19 42

(b)
1¹₁₀ h = 1 h 6 min

Total time that Billy travelled
= 1 h 6 min + 2 h 12 min
= 3 h 18 min

3 h 18 min = 3¹⁸₆₀h = 3³₁₀h

Distance between Village S and Village T
= 3³₁₀ x 110
= 363 km

Time that Brandon travelled from Village S to Village T
= 363 ÷ 60
= 6.05 h
= 6 h 3 min

6 h 3 min after 15 40 = 21 43

Time that Brandon reached Village T = 21 43

Answer: (a) 19 42; (b) 21 43