Gabriel left City G for City F at 09 30. Kylie left City G for City C at the same time. At 12 30, they were 504 km apart. Both maintained a constant speed and reached their destination at the same time at 15 20.

1. Find the distance between Cities A and C.
2. If Kylie was ³₄ the speed of Gabriel, find Gabriel's speed.

(a)
Time taken for Gabriel and Kylie to travel 09 30 to 12 30 = 3 h
Time taken for Gabriel and Kylie to travel 09 30 to 15 20 = 5 h 50 min = 5⁵⁰₆₀ h = 5⁵₆ h

Distance travelled by Gabriel and Kylie in 1 hour
= 504 ÷ 3
= 168 km

Total distance
= 5⁵₆ x 168
= 980 km

(b)
Kylie's distance : Gabriel's distance
3 : 4

Kylie's speed : Gabriel's speed
3 : 4

7 u = 168 km
1 u = 168 ÷ 7 = 24 km

Gabriel's speed
= 4 u
= 4 x 24
= 96 km/h

Answer(s): (a) 980 km; (b) 96km/h