City H and City J is 546 km apart. Liam left City H for City J at 9.00 a.m. travelling at an average speed of 78 km/h. Caden left City H later than Liam and caught up with him at 12.00 p.m. Caden was travelling at a speed of 104 km/h.

1. At what time did Caden leave City H?
2. How much later did Liam arrive in City J than Caden? Express your answer in h as a fraction or mixed number.

(a)
From 9.00 a.m. to 12.00 p.m. = 3 h

Distance that Liam covered when Caden caught up with Liam
= 3 x 78
= 234 km

Time that Caden took to travel 234 km
= 234 ÷ 104
= 2¹₄ h

1 h = 60 min
¹₄ h = ¹₄ x 60 = 15 min
2¹₄ h = 2 h 15 min

Time that Caden left City H:
2 h 15 min before 12.00 p.m. = 9.45 a.m.

(b)
Remaining distance that they had to cover to reach City J
= 546 - 234
= 312 km

Duration that Caden had to travel before reaching City J
= 312 ÷ 104
= 3 h

Duration that Liam had to travel before reaching City J
= 312 ÷ 78
= 4 h

Duration that Liam took to arrive later than Caden in City J
= 4 - 3
= 1 h

Answer(s): (a) 9.45 a.m.; (b) 1 h