Fred started driving from Town Y towards Town Z at 15 40 at an average speed of 60 km/h. Dylan began driving from Town Y towards Town Z at 18 30 at an average speed of 110 km/h.

1. At what time did Dylan pass Fred on the road?
2. 1¹₁₀ hours after passing Fred, Dylan reached Town Z. At what time did Fred reach Town Z?

(a)
From 15 40 to 18 30 = 2 h 50 min

Time that Fred travelled before Dylan started driving = 2 h 50 min

1 h = 60 min
2 h 50 min = 2⁵⁰₆₀ h = 2⁵₆ h

Distance that Fred travelled before Dylan started driving
= 2⁵₆ x 60
= ¹⁷₆ x 60
= 170 km

Difference between Dylan's and Fred's speed
= 110 - 60
= 50 km/h

Time that Dylan took to catch up with Fred
= 170 ÷ 50
= 3.4 h
= 3 h 24 min

3 h 24 min after 18 30 = 21 54

Time that Dylan passed Fred on the road = 21 54

(b)
1¹₁₀ h = 1 h 6 min

Total time that Dylan travelled
= 1 h 6 min + 3 h 24 min
= 4 h 30 min

4 h 30 min = 4³⁰₆₀h = 4¹₂h

Distance between Town Y and Town Z
= 4¹₂ x 110
= 495 km

Time that Fred travelled from Town Y to Town Z
= 495 ÷ 60
= 8.25 h
= 8 h 15 min

8 h 15 min after 15 40 = 23 55

Time that Fred reached Town Z = 23 55

Answer: (a) 21 54; (b) 23 55