City D and City E is 345 km apart. Liam left City D for City E at 8.00 a.m. travelling at an average speed of 69 km/h. Jenson left City D later than Liam and caught up with him at 11.00 a.m. Jenson was travelling at a speed of 108 km/h.

1. At what time did Jenson leave City D?
2. How much later did Liam arrive in City E than Jenson? Express your answer in h as a fraction or mixed number.

(a)
From 8.00 a.m. to 11.00 a.m. = 3 h

Distance that Liam covered when Jenson caught up with Liam
= 3 x 69
= 207 km

Time that Jenson took to travel 207 km
= 207 ÷ 108
= 1¹¹₁₂ h

1 h = 60 min
¹¹₁₂ h = ¹¹₁₂ x 60 = 55 min
1¹¹₁₂ h = 1 h 55 min

Time that Jenson left City D:
1 h 55 min before 11.00 a.m. = 9.05 a.m.

(b)
Remaining distance that they had to cover to reach City E
= 345 - 207
= 138 km

Duration that Jenson had to travel before reaching City E
= 138 ÷ 108
= 1⁵₁₈ h

Duration that Liam had to travel before reaching City E
= 138 ÷ 69
= 2 h

Duration that Liam took to arrive later than Jenson in City E
= 2 - 1⁵₁₈
= ¹³₁₈ h

Answer(s): (a) 9.05 a.m.; (b) ¹³₁₈ h