City W and City X is 684 km apart. Elijah left City W for City X at 9.00 a.m. travelling at an average speed of 76 km/h. Eric left City W later than Elijah and caught up with him at 1.00 p.m. Eric was travelling at a speed of 114 km/h.

1. At what time did Eric leave City W?
2. How much later did Elijah arrive in City X than Eric? Express your answer in h as a fraction or mixed number.

(a)
From 9.00 a.m. to 1.00 p.m. = 4 h

Distance that Elijah covered when Eric caught up with Elijah
= 4 x 76
= 304 km

Time that Eric took to travel 304 km
= 304 ÷ 114
= 2²₃ h

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

Time that Eric left City W:
2 h 40 min before 1.00 p.m. = 10.20 a.m.

(b)
Remaining distance that they had to cover to reach City X
= 684 - 304
= 380 km

Duration that Eric had to travel before reaching City X
= 380 ÷ 114
= 3¹₃ h

Duration that Elijah had to travel before reaching City X
= 380 ÷ 76
= 5 h

Duration that Elijah took to arrive later than Eric in City X
= 5 - 3¹₃
= 1²₃ h

Answer(s): (a) 10.20 a.m.; (b) 1²₃ h