Simon left City Z for City Y at 09 38. Natalie left City Z for City C at the same time. At 12 38, they were 585 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 Natalie was ⁶₇ the speed of Simon, find Simon's speed.

(a)
Time taken for Simon and Natalie to travel 09 38 to 12 38 = 3 h
Time taken for Simon and Natalie to travel 09 38 to 15 18 = 5 h 40 min = 5⁴⁰₆₀ h = 5²₃ h

Distance travelled by Simon and Natalie in 1 hour
= 585 ÷ 3
= 195 km

Total distance
= 5²₃ x 195
= 1105 km

(b)
Natalie's distance : Simon's distance
6 : 7

Natalie's speed : Simon's speed
6 : 7

13 u = 195 km
1 u = 195 ÷ 13 = 15 km

Simon's speed
= 7 u
= 7 x 15
= 105 km/h

Answer(s): (a) 1105 km; (b) 105km/h