City P and City Q are 429 km apart. At 1.17 p.m., Riordan is travelling at a uniform speed left City P for City Q while Luis set off from City Q to City P along the same road at a uniform speed, which was 11 km/h slower than that of Riordan. The two met at 4.17 p.m.

1. Find the speed of Riordan.
2. If Luis 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 Riordan and Luis to travel from 1.17 p.m. to 4.17 p.m. = 3 h

Average speed of Riordan and Luis
= 429 ÷ 3
= 143 km/h

Riordan's speed
= (143 + 11) ÷ 2
= 154 ÷ 2 
= 77 km/h

(b)
Luis's speed
= 77 - 11
= 66 km/h

Distance that Luis travelled in 3 h
= 3 x 66
= 198 km

Remaining distance that Luis needed to travel
= 429 - 198
= 231 km

Time that Luis needed to reach his destination after the two met
= 231 ÷ 66
= 3³³₆₆
= 3¹₂ h

Answer(s): (a) 77 km/h; (b) 3¹₂ h