City C and City D are 580 km apart. At 6.36 p.m., Caden is travelling at a uniform speed left City C for City D while Ken set off from City D to City C along the same road at a uniform speed, which was 12 km/h slower than that of Caden. The two met at 11.36 p.m.

1. Find the speed of Caden.
2. If Ken 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 Caden and Ken to travel from 6.36 p.m. to 11.36 p.m. = 5 h

Average speed of Caden and Ken
= 580 ÷ 5
= 116 km/h

Caden's speed
= (116 + 12) ÷ 2
= 128 ÷ 2 
= 64 km/h

(b)
Ken's speed
= 64 - 12
= 52 km/h

Distance that Ken travelled in 5 h
= 5 x 52
= 260 km

Remaining distance that Ken needed to travel
= 580 - 260
= 320 km

Time that Ken needed to reach his destination after the two met
= 320 ÷ 52
= 6⁸₅₂
= 6²₁₃ h

Answer(s): (a) 64 km/h; (b) 6²₁₃ h