City E and City F are 312 km apart. At 6.42 p.m., Valen is travelling at a uniform speed left City E for City F while Fabian set off from City F to City E along the same road at a uniform speed, which was 12 km/h slower than that of Valen. The two met at 8.42 p.m.

1. Find the speed of Valen.
2. If Fabian 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 Valen and Fabian to travel from 6.42 p.m. to 8.42 p.m. = 2 h

Average speed of Valen and Fabian
= 312 ÷ 2
= 156 km/h

Valen's speed
= (156 + 12) ÷ 2
= 168 ÷ 2 
= 84 km/h

(b)
Fabian's speed
= 84 - 12
= 72 km/h

Distance that Fabian travelled in 2 h
= 2 x 72
= 144 km

Remaining distance that Fabian needed to travel
= 312 - 144
= 168 km

Time that Fabian needed to reach his destination after the two met
= 168 ÷ 72
= 2²⁴₇₂
= 2¹₃ h

Answer(s): (a) 84 km/h; (b) 2¹₃ h