Vincent left City B for City A at 06 18. Vanessa left City B for City C at the same time. At 10 18, they were 640 km apart. Both maintained a constant speed and reached their destination at the same time at 12 15.

1. Find the distance between Cities A and C.
2. If Vanessa was ³₅ the speed of Vincent, find Vincent's speed.

(a)
Time taken for Vincent and Vanessa to travel 06 18 to 10 18 = 4 h
Time taken for Vincent and Vanessa to travel 06 18 to 12 15 = 5 h 57 min = 5⁵⁷₆₀ h = 5¹⁹₂₀ h

Distance travelled by Vincent and Vanessa in 1 hour
= 640 ÷ 4
= 160 km

Total distance
= 5¹⁹₂₀ x 160
= 952 km

(b)
Vanessa's distance : Vincent's distance
3 : 5

Vanessa's speed : Vincent's speed
3 : 5

8 u = 160 km
1 u = 160 ÷ 8 = 20 km

Vincent's speed
= 5 u
= 5 x 20
= 100 km/h

Answer(s): (a) 952 km; (b) 100km/h