Gabriel left City V for City U at 07 48. Fiona left City V for City C at the same time. At 10 48, they were 546 km apart. Both maintained a constant speed and reached their destination at the same time at 12 18.

1. Find the distance between Cities A and C.
2. If Fiona was ⁶₇ the speed of Gabriel, find Gabriel's speed.

(a)
Time taken for Gabriel and Fiona to travel 07 48 to 10 48 = 3 h
Time taken for Gabriel and Fiona to travel 07 48 to 12 18 = 4 h 30 min = 4³⁰₆₀ h = 4¹₂ h

Distance travelled by Gabriel and Fiona in 1 hour
= 546 ÷ 3
= 182 km

Total distance
= 4¹₂ x 182
= 819 km

(b)
Fiona's distance : Gabriel's distance
6 : 7

Fiona's speed : Gabriel's speed
6 : 7

13 u = 182 km
1 u = 182 ÷ 13 = 14 km

Gabriel's speed
= 7 u
= 7 x 14
= 98 km/h

Answer(s): (a) 819 km; (b) 98km/h