City X and City Y are 585 km apart. At 1.16 p.m., Ben is travelling at a uniform speed left City X for City Y while Fabian set off from City Y to City X along the same road at a uniform speed, which was 7 km/h slower than that of Ben. The two met at 6.16 p.m.

1. Find the speed of Ben.
2. If Fabian 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 Ben and Fabian to travel from 1.16 p.m. to 6.16 p.m. = 5 h

Average speed of Ben and Fabian
= 585 ÷ 5
= 117 km/h

Ben's speed
= (117 + 7) ÷ 2
= 124 ÷ 2 
= 62 km/h

(b)
Fabian's speed
= 62 - 7
= 55 km/h

Distance that Fabian travelled in 5 h
= 5 x 55
= 275 km

Remaining distance that Fabian needed to travel
= 585 - 275
= 310 km

Time that Fabian needed to reach his destination after the two met
= 310 ÷ 55
= 5³⁵₅₅
= 5⁷₁₁ h

Answer(s): (a) 62 km/h; (b) 5⁷₁₁ h