City B and City C is 390 km apart. Carl left City B for City C at 10.00 a.m. travelling at an average speed of 65 km/h. Rael left City B later than Carl and caught up with him at 12.00 p.m. Rael was travelling at a speed of 104 km/h.

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

(a)
From 10.00 a.m. to 12.00 p.m. = 2 h

Distance that Carl covered when Rael caught up with Carl
= 2 x 65
= 130 km

Time that Rael took to travel 130 km
= 130 ÷ 104
= 1¹₄ h

1 h = 60 min
¹₄ h = ¹₄ x 60 = 15 min
1¹₄ h = 1 h 15 min

Time that Rael left City B:
1 h 15 min before 12.00 p.m. = 10.45 a.m.

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

Duration that Rael had to travel before reaching City C
= 260 ÷ 104
= 2¹₂ h

Duration that Carl had to travel before reaching City C
= 260 ÷ 65
= 4 h

Duration that Carl took to arrive later than Rael in City C
= 4 - 2¹₂
= 1¹₂ h

Answer(s): (a) 10.45 a.m.; (b) 1¹₂ h