City Y and City Z are 567 km apart. At 1.42 p.m., Valen is travelling at a uniform speed left City Y for City Z while Caden set off from City Z to City Y along the same road at a uniform speed, which was 7 km/h slower than that of Valen. The two met at 4.42 p.m.

1. Find the speed of Valen.
2. If Caden 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 Valen and Caden to travel from 1.42 p.m. to 4.42 p.m. = 3 h

Average speed of Valen and Caden
= 567 ÷ 3
= 189 km/h

Valen's speed
= (189 + 7) ÷ 2
= 196 ÷ 2 
= 98 km/h

(b)
Caden's speed
= 98 - 7
= 91 km/h

Distance that Caden travelled in 3 h
= 3 x 91
= 273 km

Remaining distance that Caden needed to travel
= 567 - 273
= 294 km

Time that Caden needed to reach his destination after the two met
= 294 ÷ 91
= 3²¹₉₁
= 3³₁₃ h

Answer(s): (a) 98 km/h; (b) 3³₁₃ h