Vincent left City R for City Q at 09 46. Emma left City R for City C at the same time. At 12 46, they were 585 km apart. Both maintained a constant speed and reached their destination at the same time at 16 18.

1. Find the distance between Cities A and C.
2. If Emma was ⁷₈ the speed of Vincent, find Vincent's speed.

(a)
Time taken for Vincent and Emma to travel 09 46 to 12 46 = 3 h
Time taken for Vincent and Emma to travel 09 46 to 16 18 = 6 h 32 min = 6³²₆₀ h = 6⁸₁₅ h

Distance travelled by Vincent and Emma in 1 hour
= 585 ÷ 3
= 195 km

Total distance
= 6⁸₁₅ x 195
= 1274 km

(b)
Emma's distance : Vincent's distance
7 : 8

Emma's speed : Vincent's speed
7 : 8

15 u = 195 km
1 u = 195 ÷ 15 = 13 km

Vincent's speed
= 8 u
= 8 x 13
= 104 km/h

Answer(s): (a) 1274 km; (b) 104km/h