John started driving from City Y towards City Z at 15 40 at an average speed of 60 km/h. Andy began driving from City Y towards City Z at 17 30 at an average speed of 110 km/h.

1. At what time did Andy pass John on the road?
2. 1¹₁₀ hours after passing John, Andy reached City Z. At what time did John reach City Z?

(a)
From 15 40 to 17 30 = 1 h 50 min

Time that John travelled before Andy started driving = 1 h 50 min

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

Distance that John travelled before Andy started driving
= 1⁵₆ x 60
= ¹¹₆ x 60
= 110 km

Difference between Andy's and John's speed
= 110 - 60
= 50 km/h

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

2 h 12 min after 17 30 = 19 42

Time that Andy passed John on the road = 19 42

(b)
1¹₁₀ h = 1 h 6 min

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

3 h 18 min = 3¹⁸₆₀h = 3³₁₀h

Distance between City Y and City Z
= 3³₁₀ x 110
= 363 km

Time that John travelled from City Y to City Z
= 363 ÷ 60
= 6.05 h
= 6 h 3 min

6 h 3 min after 15 40 = 21 43

Time that John reached City Z = 21 43

Answer: (a) 19 42; (b) 21 43