Zeph started driving from Town Q towards Town R at 14 30 at an average speed of 60 km/h. Sam began driving from Town Q towards Town R at 17 20 at an average speed of 110 km/h.

1. At what time did Sam pass Zeph on the road?
2. 1¹₁₀ hours after passing Zeph, Sam reached Town R. At what time did Zeph reach Town R?

(a)
From 14 30 to 17 20 = 2 h 50 min

Time that Zeph travelled before Sam started driving = 2 h 50 min

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

Distance that Zeph travelled before Sam started driving
= 2⁵₆ x 60
= ¹⁷₆ x 60
= 170 km

Difference between Sam's and Zeph's speed
= 110 - 60
= 50 km/h

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

3 h 24 min after 17 20 = 20 44

Time that Sam passed Zeph on the road = 20 44

(b)
1¹₁₀ h = 1 h 6 min

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

4 h 30 min = 4³⁰₆₀h = 4¹₂h

Distance between Town Q and Town R
= 4¹₂ x 110
= 495 km

Time that Zeph travelled from Town Q to Town R
= 495 ÷ 60
= 8.25 h
= 8 h 15 min

8 h 15 min after 14 30 = 22 45

Time that Zeph reached Town R = 22 45

Answer: (a) 20 44; (b) 22 45