City D and City E are 585 km apart. At 4.31 p.m., Fabian is travelling at a uniform speed left City D for City E while Simon set off from City E to City D along the same road at a uniform speed, which was 5 km/h slower than that of Fabian. The two met at 7.31 p.m.

1. Find the speed of Fabian.
2. If Simon 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 Fabian and Simon to travel from 4.31 p.m. to 7.31 p.m. = 3 h

Average speed of Fabian and Simon
= 585 ÷ 3
= 195 km/h

Fabian's speed
= (195 + 5) ÷ 2
= 200 ÷ 2 
= 100 km/h

(b)
Simon's speed
= 100 - 5
= 95 km/h

Distance that Simon travelled in 3 h
= 3 x 95
= 285 km

Remaining distance that Simon needed to travel
= 585 - 285
= 300 km

Time that Simon needed to reach his destination after the two met
= 300 ÷ 95
= 3¹⁵₉₅
= 3³₁₉ h

Answer(s): (a) 100 km/h; (b) 3³₁₉ h