City P and City Q are 460 km apart. At 4.55 p.m., Michael is travelling at a uniform speed left City P for City Q while Zeph set off from City Q to City P along the same road at a uniform speed, which was 10 km/h slower than that of Michael. The two met at 6.55 p.m.

1. Find the speed of Michael.
2. If Zeph 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 Michael and Zeph to travel from 4.55 p.m. to 6.55 p.m. = 2 h

Average speed of Michael and Zeph
= 460 ÷ 2
= 230 km/h

Michael's speed
= (230 + 10) ÷ 2
= 240 ÷ 2 
= 120 km/h

(b)
Zeph's speed
= 120 - 10
= 110 km/h

Distance that Zeph travelled in 2 h
= 2 x 110
= 220 km

Remaining distance that Zeph needed to travel
= 460 - 220
= 240 km

Time that Zeph needed to reach his destination after the two met
= 240 ÷ 110
= 2²⁰₁₁₀
= 2²₁₁ h

Answer(s): (a) 120 km/h; (b) 2²₁₁ h