Luis started driving from Village M towards Village N at 15 30 at an average speed of 60 km/h. Carl began driving from Village M towards Village N at 17 20 at an average speed of 110 km/h.

1. At what time did Carl pass Luis on the road?
2. 1¹₁₀ hours after passing Luis, Carl reached Village N. At what time did Luis reach Village N?

(a)
From 15 30 to 17 20 = 1 h 50 min

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

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

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

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

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

2 h 12 min after 17 20 = 19 32

Time that Carl passed Luis on the road = 19 32

(b)
1¹₁₀ h = 1 h 6 min

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

3 h 18 min = 3¹⁸₆₀h = 3³₁₀h

Distance between Village M and Village N
= 3³₁₀ x 110
= 363 km

Time that Luis travelled from Village M to Village N
= 363 ÷ 60
= 6.05 h
= 6 h 3 min

6 h 3 min after 15 30 = 21 33

Time that Luis reached Village N = 21 33

Answer: (a) 19 32; (b) 21 33