City F and City G is 272 km apart. Archie left City F for City G at 10.00 a.m. travelling at an average speed of 68 km/h. Julian left City F later than Archie and caught up with him at 12.00 p.m. Julian was travelling at a speed of 96 km/h.

1. At what time did Julian leave City F?
2. How much later did Archie arrive in City G than Julian? 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 Archie covered when Julian caught up with Archie
= 2 x 68
= 136 km

Time that Julian took to travel 136 km
= 136 ÷ 96
= 1⁵₁₂ h

1 h = 60 min
⁵₁₂ h = ⁵₁₂ x 60 = 25 min
1⁵₁₂ h = 1 h 25 min

Time that Julian left City F:
1 h 25 min before 12.00 p.m. = 10.35 a.m.

(b)
Remaining distance that they had to cover to reach City G
= 272 - 136
= 136 km

Duration that Julian had to travel before reaching City G
= 136 ÷ 96
= 1⁵₁₂ h

Duration that Archie had to travel before reaching City G
= 136 ÷ 68
= 2 h

Duration that Archie took to arrive later than Julian in City G
= 2 - 1⁵₁₂
= ⁷₁₂ h

Answer(s): (a) 10.35 a.m.; (b) ⁷₁₂ h