City F and City G are 432 km apart. At 5.20 p.m., Luke is travelling at a uniform speed left City F for City G while Luis set off from City G to City F along the same road at a uniform speed, which was 8 km/h slower than that of Luke. The two met at 8.20 p.m.

1. Find the speed of Luke.
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 Luke and Luis to travel from 5.20 p.m. to 8.20 p.m. = 3 h

Average speed of Luke and Luis
= 432 ÷ 3
= 144 km/h

Luke's speed
= (144 + 8) ÷ 2
= 152 ÷ 2 
= 76 km/h

(b)
Luis's speed
= 76 - 8
= 68 km/h

Distance that Luis travelled in 3 h
= 3 x 68
= 204 km

Remaining distance that Luis needed to travel
= 432 - 204
= 228 km

Time that Luis needed to reach his destination after the two met
= 228 ÷ 68
= 3²⁴₆₈
= 3⁶₁₇ h

Answer(s): (a) 76 km/h; (b) 3⁶₁₇ h