City P and City Q are 585 km apart. At 1.25 p.m., Cole is travelling at a uniform speed left City P for City Q while Charlie set off from City Q to City P along the same road at a uniform speed, which was 9 km/h slower than that of Cole. The two met at 6.25 p.m.

1. Find the speed of Cole.
2. If Charlie 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 Cole and Charlie to travel from 1.25 p.m. to 6.25 p.m. = 5 h

Average speed of Cole and Charlie
= 585 ÷ 5
= 117 km/h

Cole's speed
= (117 + 9) ÷ 2
= 126 ÷ 2 
= 63 km/h

(b)
Charlie's speed
= 63 - 9
= 54 km/h

Distance that Charlie travelled in 5 h
= 5 x 54
= 270 km

Remaining distance that Charlie needed to travel
= 585 - 270
= 315 km

Time that Charlie needed to reach his destination after the two met
= 315 ÷ 54
= 5⁴⁵₅₄
= 5⁵₆ h

Answer(s): (a) 63 km/h; (b) 5⁵₆ h