Sam started driving from Town D towards Town E at 13 30 at an average speed of 60 km/h. Liam began driving from Town D towards Town E at 15 10 at an average speed of 100 km/h.

1. At what time did Liam pass Sam on the road?
2. 1¹₄ hours after passing Sam, Liam reached Town E. At what time did Sam reach Town E?

(a)
From 13 30 to 15 10 = 1 h 40 min

Time that Sam travelled before Liam started driving = 1 h 40 min

1 h = 60 min
1 h 40 min = 1⁴⁰₆₀ h = 1²₃ h

Distance that Sam travelled before Liam started driving
= 1²₃ x 60
= ⁵₃ x 60
= 100 km

Difference between Liam's and Sam's speed
= 100 - 60
= 40 km/h

Time that Liam took to catch up with Sam
= 100 ÷ 40
= 2.5 h
= 2 h 30 min

2 h 30 min after 15 10 = 17 40

Time that Liam passed Sam on the road = 17 40

(b)
1¹₄ h = 1 h 15 min

Total time that Liam travelled
= 1 h 15 min + 2 h 30 min
= 3 h 45 min

3 h 45 min = 3⁴⁵₆₀h = 3³₄h

Distance between Town D and Town E
= 3³₄ x 100
= 375 km

Time that Sam travelled from Town D to Town E
= 375 ÷ 60
= 6.25 h
= 6 h 15 min

6 h 15 min after 13 30 = 19 45

Time that Sam reached Town E = 19 45

Answer: (a) 17 40; (b) 19 45