Brandon left City Y for City X at 08 31. Cathy left City Y for City C at the same time. At 13 31, they were 800 km apart. Both maintained a constant speed and reached their destination at the same time at 15 16.

1. Find the distance between Cities A and C.
2. If Cathy was ³₅ the speed of Brandon, find Brandon's speed.

(a)
Time taken for Brandon and Cathy to travel 08 31 to 13 31 = 5 h
Time taken for Brandon and Cathy to travel 08 31 to 15 16 = 6 h 45 min = 6⁴⁵₆₀ h = 6³₄ h

Distance travelled by Brandon and Cathy in 1 hour
= 800 ÷ 5
= 160 km

Total distance
= 6³₄ x 160
= 1080 km

(b)
Cathy's distance : Brandon's distance
3 : 5

Cathy's speed : Brandon's speed
3 : 5

8 u = 160 km
1 u = 160 ÷ 8 = 20 km

Brandon's speed
= 5 u
= 5 x 20
= 100 km/h

Answer(s): (a) 1080 km; (b) 100km/h