City Z and City A is 304 km apart. Luke left City Z for City A at 11.00 a.m. travelling at an average speed of 76 km/h. Bobby left City Z later than Luke and caught up with him at 1.00 p.m. Bobby was travelling at a speed of 114 km/h.

1. At what time did Bobby leave City Z?
2. How much later did Luke arrive in City A than Bobby? 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 Luke covered when Bobby caught up with Luke
= 2 x 76
= 152 km

Time that Bobby took to travel 152 km
= 152 ÷ 114
= 1¹₃ h

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

Time that Bobby left City Z:
1 h 20 min before 1.00 p.m. = 11.40 a.m.

(b)
Remaining distance that they had to cover to reach City A
= 304 - 152
= 152 km

Duration that Bobby had to travel before reaching City A
= 152 ÷ 114
= 1¹₃ h

Duration that Luke had to travel before reaching City A
= 152 ÷ 76
= 2 h

Duration that Luke took to arrive later than Bobby in City A
= 2 - 1¹₃
= ²₃ h

Answer(s): (a) 11.40 a.m.; (b) ²₃ h