Ken started driving from City Q towards City R at 15 45 at an average speed of 60 km/h. Michael began driving from City Q towards City R at 17 35 at an average speed of 110 km/h.

1. At what time did Michael pass Ken on the road?
2. 1¹₁₀ hours after passing Ken, Michael reached City R. At what time did Ken reach City R?

(a)
From 15 45 to 17 35 = 1 h 50 min

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

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

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

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

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

2 h 12 min after 17 35 = 19 47

Time that Michael passed Ken on the road = 19 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 City Q and City R
= 3³₁₀ x 110
= 363 km

Time that Ken travelled from City Q to City R
= 363 ÷ 60
= 6.05 h
= 6 h 3 min

6 h 3 min after 15 45 = 21 48

Time that Ken reached City R = 21 48

Answer: (a) 19 47; (b) 21 48