Gabriel left City Q for City P at 09 33. Sarah left City Q for City C at the same time. At 11 33, they were 360 km apart. Both maintained a constant speed and reached their destination at the same time at 13 29.

1. Find the distance between Cities A and C.
2. If Sarah was ⁵₇ the speed of Gabriel, find Gabriel's speed.

(a)
Time taken for Gabriel and Sarah to travel 09 33 to 11 33 = 2 h
Time taken for Gabriel and Sarah to travel 09 33 to 13 29 = 3 h 56 min = 3⁵⁶₆₀ h = 3¹⁴₁₅ h

Distance travelled by Gabriel and Sarah in 1 hour
= 360 ÷ 2
= 180 km

Total distance
= 3¹⁴₁₅ x 180
= 708 km

(b)
Sarah's distance : Gabriel's distance
5 : 7

Sarah's speed : Gabriel's speed
5 : 7

12 u = 180 km
1 u = 180 ÷ 12 = 15 km

Gabriel's speed
= 7 u
= 7 x 15
= 105 km/h

Answer(s): (a) 708 km; (b) 105km/h