Gabriel started driving from Town M towards Town N at 13 45 at an average speed of 60 km/h. Michael began driving from Town M towards Town N at 15 35 at an average speed of 110 km/h.

1. At what time did Michael pass Gabriel on the road?
2. 1¹₁₀ hours after passing Gabriel, Michael reached Town N. At what time did Gabriel reach Town N?

(a)
From 13 45 to 15 35 = 1 h 50 min

Time that Gabriel travelled before Michael started driving = 1 h 50 min

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

Distance that Gabriel travelled before Michael started driving
= 1⁵₆ x 60
= ¹¹₆ x 60
= 110 km

Difference between Michael's and Gabriel's speed
= 110 - 60
= 50 km/h

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

2 h 12 min after 15 35 = 17 47

Time that Michael passed Gabriel on the road = 17 47

(b)
1¹₁₀ h = 1 h 6 min

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

3 h 18 min = 3¹⁸₆₀h = 3³₁₀h

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

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

6 h 3 min after 13 45 = 19 48

Time that Gabriel reached Town N = 19 48

Answer: (a) 17 47; (b) 19 48