Gabriel left City J for City H at 08 32. Gabby left City J for City C at the same time. At 10 32, they were 342 km apart. Both maintained a constant speed and reached their destination at the same time at 12 12.

1. Find the distance between Cities A and C.
2. If Gabby was ⁴₅ the speed of Gabriel, find Gabriel's speed.

(a)
Time taken for Gabriel and Gabby to travel 08 32 to 10 32 = 2 h
Time taken for Gabriel and Gabby to travel 08 32 to 12 12 = 3 h 40 min = 3⁴⁰₆₀ h = 3²₃ h

Distance travelled by Gabriel and Gabby in 1 hour
= 342 ÷ 2
= 171 km

Total distance
= 3²₃ x 171
= 627 km

(b)
Gabby's distance : Gabriel's distance
4 : 5

Gabby's speed : Gabriel's speed
4 : 5

9 u = 171 km
1 u = 171 ÷ 9 = 19 km

Gabriel's speed
= 5 u
= 5 x 19
= 95 km/h

Answer(s): (a) 627 km; (b) 95km/h