City W and City X is 390 km apart. Riordan left City W for City X at 11.00 a.m. travelling at an average speed of 65 km/h. Daniel left City W later than Riordan and caught up with him at 3.00 p.m. Daniel was travelling at a speed of 104 km/h.

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

(a)
From 11.00 a.m. to 3.00 p.m. = 4 h

Distance that Riordan covered when Daniel caught up with Riordan
= 4 x 65
= 260 km

Time that Daniel took to travel 260 km
= 260 ÷ 104
= 2¹₂ h

1 h = 60 min
¹₂ h = ¹₂ x 60 = 30 min
2¹₂ h = 2 h 30 min

Time that Daniel left City W:
2 h 30 min before 3.00 p.m. = 12.30 p.m.

(b)
Remaining distance that they had to cover to reach City X
= 390 - 260
= 130 km

Duration that Daniel had to travel before reaching City X
= 130 ÷ 104
= 1¹₄ h

Duration that Riordan had to travel before reaching City X
= 130 ÷ 65
= 2 h

Duration that Riordan took to arrive later than Daniel in City X
= 2 - 1¹₄
= ³₄ h

Answer(s): (a) 12.30 p.m.; (b) ³₄ h