Fabian left City C for City B at 09 49. Nicole left City C for City C at the same time. At 12 49, they were 486 km apart. Both maintained a constant speed and reached their destination at the same time at 16 39.

1. Find the distance between Cities A and C.
2. If Nicole was ⁴₅ the speed of Fabian, find Fabian's speed.

(a)
Time taken for Fabian and Nicole to travel 09 49 to 12 49 = 3 h
Time taken for Fabian and Nicole to travel 09 49 to 16 39 = 6 h 50 min = 6⁵⁰₆₀ h = 6⁵₆ h

Distance travelled by Fabian and Nicole in 1 hour
= 486 ÷ 3
= 162 km

Total distance
= 6⁵₆ x 162
= 1107 km

(b)
Nicole's distance : Fabian's distance
4 : 5

Nicole's speed : Fabian's speed
4 : 5

9 u = 162 km
1 u = 162 ÷ 9 = 18 km

Fabian's speed
= 5 u
= 5 x 18
= 90 km/h

Answer(s): (a) 1107 km; (b) 90km/h