City D and City E is 414 km apart. Liam left City D for City E at 8.00 a.m. travelling at an average speed of 69 km/h. Fred left City D later than Liam and caught up with him at 10.00 a.m. Fred was travelling at a speed of 72 km/h.

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

(a)
From 8.00 a.m. to 10.00 a.m. = 2 h

Distance that Liam covered when Fred caught up with Liam
= 2 x 69
= 138 km

Time that Fred took to travel 138 km
= 138 ÷ 72
= 1¹¹₁₂ h

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

Time that Fred left City D:
1 h 55 min before 10.00 a.m. = 8.05 a.m.

(b)
Remaining distance that they had to cover to reach City E
= 414 - 138
= 276 km

Duration that Fred had to travel before reaching City E
= 276 ÷ 72
= 3⁵₆ h

Duration that Liam had to travel before reaching City E
= 276 ÷ 69
= 4 h

Duration that Liam took to arrive later than Fred in City E
= 4 - 3⁵₆
= ¹₆ h

Answer(s): (a) 8.05 a.m.; (b) ¹₆ h