Archie left City E for City D at 09 49. Vanessa left City E for City C at the same time. At 13 49, they were 560 km apart. Both maintained a constant speed and reached their destination at the same time at 16 22.

1. Find the distance between Cities A and C.
2. If Vanessa was ⁵₉ the speed of Archie, find Archie's speed.

(a)
Time taken for Archie and Vanessa to travel 09 49 to 13 49 = 4 h
Time taken for Archie and Vanessa to travel 09 49 to 16 22 = 6 h 33 min = 6³³₆₀ h = 6¹¹₂₀ h

Distance travelled by Archie and Vanessa in 1 hour
= 560 ÷ 4
= 140 km

Total distance
= 6¹¹₂₀ x 140
= 917 km

(b)
Vanessa's distance : Archie's distance
5 : 9

Vanessa's speed : Archie's speed
5 : 9

14 u = 140 km
1 u = 140 ÷ 14 = 10 km

Archie's speed
= 9 u
= 9 x 10
= 90 km/h

Answer(s): (a) 917 km; (b) 90km/h