Riordan left City Z for City Y at 09 16. Natalie left City Z for City C at the same time. At 12 16, they were 504 km apart. Both maintained a constant speed and reached their destination at the same time at 15 11.

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

(a)
Time taken for Riordan and Natalie to travel 09 16 to 12 16 = 3 h
Time taken for Riordan and Natalie to travel 09 16 to 15 11 = 5 h 55 min = 5⁵⁵₆₀ h = 5¹¹₁₂ h

Distance travelled by Riordan and Natalie in 1 hour
= 504 ÷ 3
= 168 km

Total distance
= 5¹¹₁₂ x 168
= 994 km

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

Natalie's speed : Riordan's speed
3 : 5

8 u = 168 km
1 u = 168 ÷ 8 = 21 km

Riordan's speed
= 5 u
= 5 x 21
= 105 km/h

Answer(s): (a) 994 km; (b) 105km/h