Luke started driving from Village J towards Village K at 13 30 at an average speed of 60 km/h. John began driving from Village J towards Village K at 15 20 at an average speed of 110 km/h.

1. At what time did John pass Luke on the road?
2. 1¹₁₀ hours after passing Luke, John reached Village K. At what time did Luke reach Village K?

(a)
From 13 30 to 15 20 = 1 h 50 min

Time that Luke travelled before John started driving = 1 h 50 min

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

Distance that Luke travelled before John started driving
= 1⁵₆ x 60
= ¹¹₆ x 60
= 110 km

Difference between John's and Luke's speed
= 110 - 60
= 50 km/h

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

2 h 12 min after 15 20 = 17 32

Time that John passed Luke on the road = 17 32

(b)
1¹₁₀ h = 1 h 6 min

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

3 h 18 min = 3¹⁸₆₀h = 3³₁₀h

Distance between Village J and Village K
= 3³₁₀ x 110
= 363 km

Time that Luke travelled from Village J to Village K
= 363 ÷ 60
= 6.05 h
= 6 h 3 min

6 h 3 min after 13 30 = 19 33

Time that Luke reached Village K = 19 33

Answer: (a) 17 32; (b) 19 33