City D and City E is 539 km apart. Carl left City D for City E at 11.00 a.m. travelling at an average speed of 77 km/h. Peter left City D later than Carl and caught up with him at 1.00 p.m. Peter was travelling at a speed of 84 km/h.

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

(a)
From 11.00 a.m. to 1.00 p.m. = 2 h

Distance that Carl covered when Peter caught up with Carl
= 2 x 77
= 154 km

Time that Peter took to travel 154 km
= 154 ÷ 84
= 1⁵₆ h

1 h = 60 min
⁵₆ h = ⁵₆ x 60 = 50 min
1⁵₆ h = 1 h 50 min

Time that Peter left City D:
1 h 50 min before 1.00 p.m. = 11.10 a.m.

(b)
Remaining distance that they had to cover to reach City E
= 539 - 154
= 385 km

Duration that Peter had to travel before reaching City E
= 385 ÷ 84
= 4⁷₁₂ h

Duration that Carl had to travel before reaching City E
= 385 ÷ 77
= 5 h

Duration that Carl took to arrive later than Peter in City E
= 5 - 4⁷₁₂
= ⁵₁₂ h

Answer(s): (a) 11.10 a.m.; (b) ⁵₁₂ h