City A and City B is 420 km apart. Luke left City A for City B at 9.00 a.m. travelling at an average speed of 60 km/h. Henry left City A later than Luke and caught up with him at 11.00 a.m. Henry was travelling at a speed of 90 km/h.

1. At what time did Henry leave City A?
2. How much later did Luke arrive in City B than Henry? Express your answer in h as a fraction or mixed number.

(a)
From 9.00 a.m. to 11.00 a.m. = 2 h

Distance that Luke covered when Henry caught up with Luke
= 2 x 60
= 120 km

Time that Henry took to travel 120 km
= 120 ÷ 90
= 1¹₃ h

1 h = 60 min
¹₃ h = ¹₃ x 60 = 20 min
1¹₃ h = 1 h 20 min

Time that Henry left City A:
1 h 20 min before 11.00 a.m. = 9.40 a.m.

(b)
Remaining distance that they had to cover to reach City B
= 420 - 120
= 300 km

Duration that Henry had to travel before reaching City B
= 300 ÷ 90
= 3¹₃ h

Duration that Luke had to travel before reaching City B
= 300 ÷ 60
= 5 h

Duration that Luke took to arrive later than Henry in City B
= 5 - 3¹₃
= 1²₃ h

Answer(s): (a) 9.40 a.m.; (b) 1²₃ h