City F and City G is 420 km apart. Riordan left City F for City G at 11.00 a.m. travelling at an average speed of 70 km/h. Jack left City F later than Riordan and caught up with him at 3.00 p.m. Jack was travelling at a speed of 112 km/h.

1. At what time did Jack leave City F?
2. How much later did Riordan arrive in City G than Jack? 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 Jack caught up with Riordan
= 4 x 70
= 280 km

Time that Jack took to travel 280 km
= 280 ÷ 112
= 2¹₂ h

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

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

(b)
Remaining distance that they had to cover to reach City G
= 420 - 280
= 140 km

Duration that Jack had to travel before reaching City G
= 140 ÷ 112
= 1¹₄ h

Duration that Riordan had to travel before reaching City G
= 140 ÷ 70
= 2 h

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

Answer(s): (a) 12.30 p.m.; (b) ³₄ h