City L and City M are 380 km apart. At 3.29 p.m., Luis is travelling at a uniform speed left City L for City M while Billy set off from City M to City L along the same road at a uniform speed, which was 10 km/h slower than that of Luis. The two met at 5.29 p.m.

1. Find the speed of Luis.
2. If Billy 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 Luis and Billy to travel from 3.29 p.m. to 5.29 p.m. = 2 h

Average speed of Luis and Billy
= 380 ÷ 2
= 190 km/h

Luis's speed
= (190 + 10) ÷ 2
= 200 ÷ 2 
= 100 km/h

(b)
Billy's speed
= 100 - 10
= 90 km/h

Distance that Billy travelled in 2 h
= 2 x 90
= 180 km

Remaining distance that Billy needed to travel
= 380 - 180
= 200 km

Time that Billy needed to reach his destination after the two met
= 200 ÷ 90
= 2²⁰₉₀
= 2²₉ h

Answer(s): (a) 100 km/h; (b) 2²₉ h