Oscar left City Z for City Y at 08 27. Vanessa left City Z for City C at the same time. At 12 27, they were 720 km apart. Both maintained a constant speed and reached their destination at the same time at 15 18.

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

(a)
Time taken for Oscar and Vanessa to travel 08 27 to 12 27 = 4 h
Time taken for Oscar and Vanessa to travel 08 27 to 15 18 = 6 h 51 min = 6⁵¹₆₀ h = 6¹⁷₂₀ h

Distance travelled by Oscar and Vanessa in 1 hour
= 720 ÷ 4
= 180 km

Total distance
= 6¹⁷₂₀ x 180
= 1233 km

(b)
Vanessa's distance : Oscar's distance
4 : 5

Vanessa's speed : Oscar's speed
4 : 5

9 u = 180 km
1 u = 180 ÷ 9 = 20 km

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

Answer(s): (a) 1233 km; (b) 100km/h