City T and City U are 374 km apart. At 5.59 p.m., Xavier is travelling at a uniform speed left City T for City U while Michael set off from City U to City T along the same road at a uniform speed, which was 11 km/h slower than that of Xavier. The two met at 7.59 p.m.

1. Find the speed of Xavier.
2. If Michael 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 Xavier and Michael to travel from 5.59 p.m. to 7.59 p.m. = 2 h

Average speed of Xavier and Michael
= 374 ÷ 2
= 187 km/h

Xavier's speed
= (187 + 11) ÷ 2
= 198 ÷ 2 
= 99 km/h

(b)
Michael's speed
= 99 - 11
= 88 km/h

Distance that Michael travelled in 2 h
= 2 x 88
= 176 km

Remaining distance that Michael needed to travel
= 374 - 176
= 198 km

Time that Michael needed to reach his destination after the two met
= 198 ÷ 88
= 2²²₈₈
= 2¹₄ h

Answer(s): (a) 99 km/h; (b) 2¹₄ h