Michael started driving from Town P towards Town Q at 13 30 at an average speed of 60 km/h. Tom began driving from Town P towards Town Q at 15 20 at an average speed of 110 km/h.

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

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

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

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

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

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

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

2 h 12 min after 15 20 = 17 32

Time that Tom passed Michael on the road = 17 32

(b)
1¹₁₀ h = 1 h 6 min

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

3 h 18 min = 3¹⁸₆₀h = 3³₁₀h

Distance between Town P and Town Q
= 3³₁₀ x 110
= 363 km

Time that Michael travelled from Town P to Town Q
= 363 ÷ 60
= 6.05 h
= 6 h 3 min

6 h 3 min after 13 30 = 19 33

Time that Michael reached Town Q = 19 33

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