City C and City D is 468 km apart. Ryan left City C for City D at 8.00 a.m. travelling at an average speed of 78 km/h. Valen left City C later than Ryan and caught up with him at 11.00 a.m. Valen was travelling at a speed of 104 km/h.

1. At what time did Valen leave City C?
2. How much later did Ryan arrive in City D than Valen? Express your answer in h as a fraction or mixed number.

(a)
From 8.00 a.m. to 11.00 a.m. = 3 h

Distance that Ryan covered when Valen caught up with Ryan
= 3 x 78
= 234 km

Time that Valen 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 Valen left City C:
2 h 15 min before 11.00 a.m. = 8.45 a.m.

(b)
Remaining distance that they had to cover to reach City D
= 468 - 234
= 234 km

Duration that Valen had to travel before reaching City D
= 234 ÷ 104
= 2¹₄ h

Duration that Ryan had to travel before reaching City D
= 234 ÷ 78
= 3 h

Duration that Ryan took to arrive later than Valen in City D
= 3 - 2¹₄
= ³₄ h

Answer(s): (a) 8.45 a.m.; (b) ³₄ h