Peter left City C for City B at 06 49. Natalie left City C for City C at the same time. At 10 49, they were 640 km apart. Both maintained a constant speed and reached their destination at the same time at 12 16.

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

(a)
Time taken for Peter and Natalie to travel 06 49 to 10 49 = 4 h
Time taken for Peter and Natalie to travel 06 49 to 12 16 = 5 h 27 min = 5²⁷₆₀ h = 5⁹₂₀ h

Distance travelled by Peter and Natalie in 1 hour
= 640 ÷ 4
= 160 km

Total distance
= 5⁹₂₀ x 160
= 872 km

(b)
Natalie's distance : Peter's distance
3 : 5

Natalie's speed : Peter's speed
3 : 5

8 u = 160 km
1 u = 160 ÷ 8 = 20 km

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

Answer(s): (a) 872 km; (b) 100km/h