City F and City G are 460 km apart. At 6.19 p.m., Simon is travelling at a uniform speed left City F for City G while Archie set off from City G to City F along the same road at a uniform speed, which was 10 km/h slower than that of Simon. The two met at 8.19 p.m.

1. Find the speed of Simon.
2. If Archie continued to travel at the same speed, how long would it take for him to reach his destination after the two met? Express your answer in mixed number.

(a)
Time taken for Simon and Archie to travel from 6.19 p.m. to 8.19 p.m. = 2 h

Average speed of Simon and Archie
= 460 ÷ 2
= 230 km/h

Simon's speed
= (230 + 10) ÷ 2
= 240 ÷ 2 
= 120 km/h

(b)
Archie's speed
= 120 - 10
= 110 km/h

Distance that Archie travelled in 2 h
= 2 x 110
= 220 km

Remaining distance that Archie needed to travel
= 460 - 220
= 240 km

Time that Archie needed to reach his destination after the two met
= 240 ÷ 110
= 2²⁰₁₁₀
= 2²₁₁ h

Answer(s): (a) 120 km/h; (b) 2²₁₁ h