Gabriel left City C for City B at 07 44. Julie left City C for City C at the same time. At 10 44, they were 540 km apart. Both maintained a constant speed and reached their destination at the same time at 13 36.

1. Find the distance between Cities A and C.
2. If Julie was ⁷₈ the speed of Gabriel, find Gabriel's speed.

(a)
Time taken for Gabriel and Julie to travel 07 44 to 10 44 = 3 h
Time taken for Gabriel and Julie to travel 07 44 to 13 36 = 5 h 52 min = 5⁵²₆₀ h = 5¹³₁₅ h

Distance travelled by Gabriel and Julie in 1 hour
= 540 ÷ 3
= 180 km

Total distance
= 5¹³₁₅ x 180
= 1056 km

(b)
Julie's distance : Gabriel's distance
7 : 8

Julie's speed : Gabriel's speed
7 : 8

15 u = 180 km
1 u = 180 ÷ 15 = 12 km

Gabriel's speed
= 8 u
= 8 x 12
= 96 km/h

Answer(s): (a) 1056 km; (b) 96km/h