City D and City E are 408 km apart. At 5.16 p.m., Archie is travelling at a uniform speed left City D for City E while Pierre set off from City E to City D along the same road at a uniform speed, which was 10 km/h slower than that of Archie. The two met at 8.16 p.m.

1. Find the speed of Archie.
2. If Pierre 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 Archie and Pierre to travel from 5.16 p.m. to 8.16 p.m. = 3 h

Average speed of Archie and Pierre
= 408 ÷ 3
= 136 km/h

Archie's speed
= (136 + 10) ÷ 2
= 146 ÷ 2 
= 73 km/h

(b)
Pierre's speed
= 73 - 10
= 63 km/h

Distance that Pierre travelled in 3 h
= 3 x 63
= 189 km

Remaining distance that Pierre needed to travel
= 408 - 189
= 219 km

Time that Pierre needed to reach his destination after the two met
= 219 ÷ 63
= 3³⁰₆₃
= 3¹⁰₂₁ h

Answer(s): (a) 73 km/h; (b) 3¹⁰₂₁ h