City F and City G are 450 km apart. At 4.40 p.m., Pierre is travelling at a uniform speed left City F for City G while Vincent set off from City G to City F along the same road at a uniform speed, which was 10 km/h slower than that of Pierre. The two met at 7.40 p.m.

1. Find the speed of Pierre.
2. If Vincent 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 Pierre and Vincent to travel from 4.40 p.m. to 7.40 p.m. = 3 h

Average speed of Pierre and Vincent
= 450 ÷ 3
= 150 km/h

Pierre's speed
= (150 + 10) ÷ 2
= 160 ÷ 2 
= 80 km/h

(b)
Vincent's speed
= 80 - 10
= 70 km/h

Distance that Vincent travelled in 3 h
= 3 x 70
= 210 km

Remaining distance that Vincent needed to travel
= 450 - 210
= 240 km

Time that Vincent needed to reach his destination after the two met
= 240 ÷ 70
= 3³⁰₇₀
= 3³₇ h

Answer(s): (a) 80 km/h; (b) 3³₇ h