City D and City E is 544 km apart. Ken left City D for City E at 10.00 a.m. travelling at an average speed of 68 km/h. Perry left City D later than Ken and caught up with him at 2.00 p.m. Perry was travelling at a speed of 102 km/h.

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

(a)
From 10.00 a.m. to 2.00 p.m. = 4 h

Distance that Ken covered when Perry caught up with Ken
= 4 x 68
= 272 km

Time that Perry took to travel 272 km
= 272 ÷ 102
= 2²₃ h

1 h = 60 min
²₃ h = ²₃ x 60 = 40 min
2²₃ h = 2 h 40 min

Time that Perry left City D:
2 h 40 min before 2.00 p.m. = 11.20 a.m.

(b)
Remaining distance that they had to cover to reach City E
= 544 - 272
= 272 km

Duration that Perry had to travel before reaching City E
= 272 ÷ 102
= 2²₃ h

Duration that Ken had to travel before reaching City E
= 272 ÷ 68
= 4 h

Duration that Ken took to arrive later than Perry in City E
= 4 - 2²₃
= 1¹₃ h

Answer(s): (a) 11.20 a.m.; (b) 1¹₃ h