City M and City N are 342 km apart. At 4.20 p.m., Vaidev is travelling at a uniform speed left City M for City N while Archie set off from City N to City M along the same road at a uniform speed, which was 12 km/h slower than that of Vaidev. The two met at 7.20 p.m.

1. Find the speed of Vaidev.
2. If Archie 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 Vaidev and Archie to travel from 4.20 p.m. to 7.20 p.m. = 3 h

Average speed of Vaidev and Archie
= 342 ÷ 3
= 114 km/h

Vaidev's speed
= (114 + 12) ÷ 2
= 126 ÷ 2 
= 63 km/h

(b)
Archie's speed
= 63 - 12
= 51 km/h

Distance that Archie travelled in 3 h
= 3 x 51
= 153 km

Remaining distance that Archie needed to travel
= 342 - 153
= 189 km

Time that Archie needed to reach his destination after the two met
= 189 ÷ 51
= 3³⁶₅₁
= 3¹²₁₇ h

Answer(s): (a) 63 km/h; (b) 3¹²₁₇ h