Michael left City C for City B at 08 45. Gillian left City C for City C at the same time. At 11 45, they were 468 km apart. Both maintained a constant speed and reached their destination at the same time at 13 15.

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

(a)
Time taken for Michael and Gillian to travel 08 45 to 11 45 = 3 h
Time taken for Michael and Gillian to travel 08 45 to 13 15 = 4 h 30 min = 4³⁰₆₀ h = 4¹₂ h

Distance travelled by Michael and Gillian in 1 hour
= 468 ÷ 3
= 156 km

Total distance
= 4¹₂ x 156
= 702 km

(b)
Gillian's distance : Michael's distance
5 : 7

Gillian's speed : Michael's speed
5 : 7

12 u = 156 km
1 u = 156 ÷ 12 = 13 km

Michael's speed
= 7 u
= 7 x 13
= 91 km/h

Answer(s): (a) 702 km; (b) 91km/h