City D and City E is 320 km apart. Carl left City D for City E at 11.00 a.m. travelling at an average speed of 64 km/h. Valen left City D later than Carl and caught up with him at 1.00 p.m. Valen was travelling at a speed of 96 km/h.

1. At what time did Valen leave City D?
2. How much later did Carl arrive in City E than Valen? 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 Carl covered when Valen caught up with Carl
= 2 x 64
= 128 km

Time that Valen took to travel 128 km
= 128 ÷ 96
= 1¹₃ h

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

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

(b)
Remaining distance that they had to cover to reach City E
= 320 - 128
= 192 km

Duration that Valen had to travel before reaching City E
= 192 ÷ 96
= 2 h

Duration that Carl had to travel before reaching City E
= 192 ÷ 64
= 3 h

Duration that Carl took to arrive later than Valen in City E
= 3 - 2
= 1 h

Answer(s): (a) 11.40 a.m.; (b) 1 h