Luis started driving from Town H towards Town J at 13 40 at an average speed of 60 km/h. Luke began driving from Town H towards Town J at 15 30 at an average speed of 110 km/h.

1. At what time did Luke pass Luis on the road?
2. 1¹₁₀ hours after passing Luis, Luke reached Town J. At what time did Luis reach Town J?

(a)
From 13 40 to 15 30 = 1 h 50 min

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

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

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

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

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

2 h 12 min after 15 30 = 17 42

Time that Luke passed Luis on the road = 17 42

(b)
1¹₁₀ h = 1 h 6 min

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

3 h 18 min = 3¹⁸₆₀h = 3³₁₀h

Distance between Town H and Town J
= 3³₁₀ x 110
= 363 km

Time that Luis travelled from Town H to Town J
= 363 ÷ 60
= 6.05 h
= 6 h 3 min

6 h 3 min after 13 40 = 19 43

Time that Luis reached Town J = 19 43

Answer: (a) 17 42; (b) 19 43