Archie left City C for City B at 09 45. Nicole left City C for City C at the same time. At 13 45, they were 768 km apart. Both maintained a constant speed and reached their destination at the same time at 15 35.

1. Find the distance between Cities A and C.
2. If Nicole was ⁵₇ the speed of Archie, find Archie's speed.

(a)
Time taken for Archie and Nicole to travel 09 45 to 13 45 = 4 h
Time taken for Archie and Nicole to travel 09 45 to 15 35 = 5 h 50 min = 5⁵⁰₆₀ h = 5⁵₆ h

Distance travelled by Archie and Nicole in 1 hour
= 768 ÷ 4
= 192 km

Total distance
= 5⁵₆ x 192
= 1120 km

(b)
Nicole's distance : Archie's distance
5 : 7

Nicole's speed : Archie's speed
5 : 7

12 u = 192 km
1 u = 192 ÷ 12 = 16 km

Archie's speed
= 7 u
= 7 x 16
= 112 km/h

Answer(s): (a) 1120 km; (b) 112km/h